Business, Sauder School of
Organizational Behaviour and Human Resources, Division of
DSpace
UBCV
Ma, Dennis George
Doctor of Philosophy - PhD
University of British Columbia
Platforms are increasingly the nexuses of economic activity and social organization; making them important sociologically and managerially. The strategic management and organizations literature remains concerned with inter-platform competition, which is viewed as being determined by platforms’ underlying network size—the core tenet of extant platform theory. Emerging research increasingly challenges longstanding assumptions underlying dominant platform views; suggesting that network organization supersedes the determinance of network size. Although we know platform network organization matters, current literature remains absent theory to formalize this critical element of platform dynamics. This dissertation extends network ecology approaches to formalize a framework for analyzing platforms’ network activity dynamics to address the research question: how is platform activity organized? I initialize a network dynamic view of the platform by centering on the organization of platform activity from a topological perspective while embracing heterogeneity in platform environments and network configurations. Specifically, this dissertation focuses on the relationship between platforms’ activity integration and growth. I develop a platform network theory of connectance, centralization, clustering, centralized clustering, and cross-functionality. These five Cs provide an initial representation of network organization under a long-due framework for activity-oriented network dynamic platform analysis. Using latent growth modeling with comprehensive fixed effects on complete and granular Ethereum Metropolis blockchain network data from October 17, 2017 to January 1, 2020 drawn from the 200 highest activity contracts, this dissertation empirically examines the relation of the five network properties on platform activity growth. The results show nuanced support for network organization increasing activity growth. This dissertation lays the groundwork for a network dynamic platform paradigm and has the potential to significantly guide both platform theory and practice. The dynamic, activity-oriented, network perspective put forth here directly challenges the static, size-fixated, black box approach dominating the current platforms literature. This dissertation demonstrates that the ways in which platform activity are organized impacts activity growth. Future research should re-evaluate assumptions around platform network size and incorporate activity dynamics. Practical implications follow accordingly: managers should focus on activity organization (i.e., quality) and re-evaluate the “get big fast” (i.e., quantity) prescription directing the platform management discourse for the past two decades.
TOWARD A NETWORK DYNAMIC VIEW OF THE PLATFORM by Dennis George Ma A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Business Administration – Organizational Behaviour) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) July 2023 © Dennis George Ma, 2023ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: TOWARD A NETWORK DYNAMIC VIEW OF THE PLATFORM submitted by Dennis George Ma in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Business Administration – Organizational Behaviour Examining Committee: Marc-David Seidel, Associate Professor, Business Administration, UBC Supervisor Danielle van Jaarsveld, Associate Professor, Business Administration, UBC Co-supervisor Gene Moo Lee, Associate Professor, Business Administration, UBC Supervisory Committee Member Ning Nan, Associate Professor, Business Administration, UBC University Examiner Chen Feng, Associate Professor, Electrical Engineering, UBC (Okanagan) University Examiner Kim Bates, Associate Professor, Business Administration, TMU External Examiner Additional Supervisory Committee Members: David Walker, Assistant Professor, Management, UBC (Okanagan) Supervisory Committee Member Chris Rowell, Principal, Performance Frontiers Supervisory Committee Member iii ABSTRACT Platforms are increasingly the nexuses of economic activity and social organization; making them important sociologically and managerially. The strategic management and organizations literature remains concerned with inter-platform competition, which is viewed as being determined by platforms’ underlying network size—the core tenet of extant platform theory. Emerging research increasingly challenges longstanding assumptions underlying dominant platform views; suggesting that network organization supersedes the determinance of network size. Although we know platform network organization matters, current literature remains absent theory to formalize this critical element of platform dynamics. This dissertation extends network ecology approaches to formalize a framework for analyzing platforms’ network activity dynamics to address the research question: how is platform activity organized? I initialize a network dynamic view of the platform by centering on the organization of platform activity from a topological perspective while embracing heterogeneity in platform environments and network configurations. Specifically, this dissertation focuses on the relationship between platforms’ activity integration and growth. I develop a platform network theory of connectance, centralization, clustering, centralized clustering, and cross-functionality. These five Cs provide an initial representation of network organization under a long-due framework for activity-oriented network dynamic platform analysis. Using latent growth modeling with comprehensive fixed effects on complete and granular Ethereum Metropolis blockchain network data from October 17, 2017 to January 1, 2020 drawn from the 200 highest activity contracts, this dissertation empirically examines the relation of the five network properties on platform activity growth. The results show nuanced support for network organization increasing activity growth. This dissertation lays the groundwork for a network dynamic platform paradigm and has the potential to significantly guide both platform theory and practice. The dynamic, activity-oriented, network perspective put forth here directly challenges the static, size-fixated, black box approach dominating the current platforms literature. This dissertation demonstrates that the ways in which platform activity are organized impacts activity growth. Future research should re-evaluate assumptions around platform network size and incorporate activity dynamics. Practical implications follow accordingly: managers should focus on activity organization (i.e., quality) and re-evaluate the “get big fast” (i.e., quantity) prescription directing the platform management discourse for the past two decades. iv LAY SUMMARY Platforms permeate social life. Platforms create value by connecting their network of users and providers (e.g., of products, services, etc.). The quantity of potential connections within a platform network grows exponentially with the size of the network. In business, platform strategy focuses on one network goal: get big, fast. However, just because network connections can be made does not mean that they will be made. Evidence suggests that the ways in which platform networks organize is a key element in understanding how platforms develop and progress. Yet, there is no formalized approach to make sense of such network organizational dynamics. This dissertation’s key goal is establishing a framework for analyzing platforms’ actual network organizational dynamics. By examining how platform activity organizes—rejecting network size-based hypotheticals—this dissertation lays the groundwork for an approach centered on actual network qualities, over supposed quantities. The framework enhances platform management in research and practice. v PREFACE This dissertation is original, unpublished, independent work by the author, D. G. Ma. vi TABLE OF CONTENTS ABSTRACT ................................................................................................................................... iii LAY SUMMARY .......................................................................................................................... iv PREFACE ....................................................................................................................................... v TABLE OF CONTENTS ............................................................................................................... vi LIST OF TABLES ......................................................................................................................... ix LIST OF FIGURES ........................................................................................................................ x LIST OF ABBREVIATIONS ........................................................................................................ xi GLOSSARY ................................................................................................................................. xii ACKNOWLEDGEMENTS ......................................................................................................... xiv DEDICATION ............................................................................................................................. xvi CHAPTER 1: INTRODUCTION ................................................................................................... 1 Background ................................................................................................................................. 1 Research Question and Motivation ............................................................................................. 3 Dissertation Structure ................................................................................................................ 12 Contributions ............................................................................................................................. 12 CHAPTER 2: LITERATURE REVIEW ...................................................................................... 19 Platforms Contextualized .......................................................................................................... 19 Platform Research Roots ........................................................................................................... 21 Industrial economics: Platforms as multisided markets (MSMs) .......................................... 21 Technology management: Platforms as technological architectures.................................... 22 Towards a Generalized Conceptualization ................................................................................ 24 Structural definition ............................................................................................................... 28 Component function ............................................................................................................... 29 Platform function ................................................................................................................... 30 Competitive logic ................................................................................................................... 31 Strategic emphasis ................................................................................................................. 33 Definition .................................................................................................................................. 37 Conceptual Boundaries ............................................................................................................. 39 Technology Management Emphases ......................................................................................... 40 Industrial Economics Emphases ............................................................................................... 42 vii The Role of Networks ............................................................................................................... 45 CHAPTER 3: THEORETICAL DEVELOPMENT ..................................................................... 49 Opening the Platform Network “Black Box” ............................................................................ 49 Adopting a Network Ecology Approach to Platform Analysis ................................................. 52 Network Activity Framework ................................................................................................... 54 Network Topology and Mechanisms ........................................................................................ 60 Dynamic Network Topology ..................................................................................................... 64 Analytical Approach ................................................................................................................. 69 Connectance .............................................................................................................................. 72 Centralization ............................................................................................................................ 77 Clustering .................................................................................................................................. 85 Centralized Clustering ............................................................................................................... 88 Cross-functionality .................................................................................................................... 92 CHAPTER 4: METHODS ............................................................................................................ 97 Ethereum Blockchain ................................................................................................................ 97 Data ........................................................................................................................................... 99 Statistical Software .................................................................................................................. 103 Measures.................................................................................................................................. 103 Dependent variable .............................................................................................................. 103 Independent variables .......................................................................................................... 104 Data Preparation ...................................................................................................................... 112 Analysis ................................................................................................................................... 114 CHAPTER 5: RESULTS ............................................................................................................ 120 Size (Model 1) ......................................................................................................................... 122 Connectance (Model 2) ........................................................................................................... 122 Centralization (Model 3) ......................................................................................................... 124 Clustering (Model 4) ............................................................................................................... 125 Centralized Clustering (Model 5) ............................................................................................ 125 Cross-functionality (Model 6) ................................................................................................. 126 Robustness Checks .................................................................................................................. 131 Lower 50% subsample without constant terms (Model 8) .................................................. 134 Lower 50% subsample with constant terms (Model 9)........................................................ 135 viii CHAPTER 6: DISCUSSION AND CONCLUSION ................................................................. 140 Theoretical Contributions ........................................................................................................ 140 Activity as primary analytical unit ...................................................................................... 141 Formalizing platform network theory.................................................................................. 142 Structure, not just size ......................................................................................................... 143 Blockchain data: A promising empirical opportunity ......................................................... 145 Limitations .............................................................................................................................. 146 Future Research ....................................................................................................................... 151 Extending contemporary network theory ............................................................................ 151 Integrating platforms research ............................................................................................ 153 Integrating with existing theory ........................................................................................... 154 Incorporating environment .................................................................................................. 156 Practical Contributions and Implications ................................................................................ 158 Conclusion ............................................................................................................................... 163 REFERENCES ........................................................................................................................... 168 APPENDIX A: Niche Crowding ................................................................................................ 186 ix LIST OF TABLES Table 2-1: Platform literature summary .................................................................................... 26 Table 2-2: Comparison of platform conceptualizations ............................................................ 36 Table 3-1: Summary of extant platform perspectives versus proposed perspective ................. 52 Table 3-2: Platform, interaction, and component examples...................................................... 60 Table 4-1: Top 10 Ethereum (Metropolis) addresses by transaction volume (10/16/2017-1/1/2020) ................................................................................................................................... 99 Table 4-2: Descriptive statistics .............................................................................................. 119 Table 4-3: Correlation matrix .................................................................................................. 119 Table 5-1: Latent growth model results .................................................................................. 121 Table 5-2: Latent growth model results (robustness checks) .................................................. 132 x LIST OF FIGURES Figure 3-1: Network topology example .................................................................................... 61 Figure 3-2: Centralized star and regular ring networks............................................................. 63 Figure 3-3: Integrative variability in network efficiency and scale .......................................... 67 Figure 3-4: Relational dynamics between network integration and activity ............................. 70 Figure 3-5: High versus low network connectance ................................................................... 74 Figure 3-6: Scale-free and random graph topologies and associated density distributions and associated density distributions ................................................................................................. 79 Figure 3-7: High versus low network clustering ....................................................................... 85 Figure 3-8: High centrality ........................................................................................................ 88 Figure 3-9: Network flow base motifs ...................................................................................... 93 Figure 4-1: Weekly activity of the 10 highest volume Ethereum Metropolis contracts ......... 102 Figure 4-2: Weekly activity of the 10 highest volume Ethereum Metropolis contracts (natural log transformed) ...................................................................................................................... 104 Figure 4-3: Latent growth curve model with slope loading scores ......................................... 116 Figure 4-4: Illustration of latent growth curve modeling approach ........................................ 118 Figure 5-1: Latent activity growth trajectories by size (high vs. low) .................................... 127 Figure 5-2: Latent activity growth trajectories by connectance (high vs. low)....................... 128 Figure 5-3: Latent activity growth trajectories by centralization (high vs. low) .................... 128 Figure 5-4: Latent activity growth trajectories by clustering (high vs. low)........................... 129 Figure 5-5: Latent activity growth trajectories by cross-functionality (high vs. low) ............ 129 Figure 5-6: Latent activity growth trajectories by positive coefficients (high vs. low) .......... 130 Figure A-1: Area of overlapping between two circles of different sizes ................................ 188 xi LIST OF ABBREVIATIONS Abbreviation Definition LGM Latent growth model MSM Multisided market MSP Multisided platform SEM Structural equation modeling xii GLOSSARY Term Definition Centralization the degree to which a network’s connections are asymmetrically distributed among components. Centralized Clustering the degree to which a network exhibits clustering among high centrality components. Clustering the degree to which a network exhibits interconnected subgroups/communities. Component an entity systematized by the platform. Components generally take the form of a complement (good or service representation) or complementor (complement producer). Users (individuals or organizations that instantiate platform activity) are also categorized as components in this dissertation due to its aim of a highly general perspective. Connectance the number of connections on a network. Cross-functionality the degree to which components in a network exhibit functional diversity. Dynamics forces or processes that produce [or inhibit] change inside a group or system ("Dynamics," n.d.). Outcomes are also a part of dynamics. More specifically, this dissertation examines how activity organization or flows (i.e., as antecedent) impact subsequent activity stocks (i.e., as outcome). The ways in which these stocks are organized then carry implications for subsequent stocks, and so on and so forth. Network size the number of components on a network. Network structure the organization of connections between network components. This dissertation focuses on component-to-component interactions as the connections which form the broader network structure—which can be multifaceted. This dissertation specifically elaborates on connectance, centralization, clustering, centralized clustering, and cross-functionality to characterize network structure. Platform an entity that systematizes (i.e., enables, mediates, and constrains) components and/or component activity through authentication (i.e., validation). xiii Platform network the components systematized by a given platform. Platform networks contain various properties such as size, structure, and activity. Platform (network) activity the activity realized through a platform (i.e., platform use). A single instance of activity refers to an action that is mediated (i.e., made possible) by the platform. Two key forms of activity discussed throughout this dissertation are interactions (component to component activity) and innovations (the addition of a new component to the platform). Empirically, activity is contextualized by the platform (e.g., a transaction on a credit card platform, a booking on a travel platform, a message on a messaging platform, etc.). *most definitions are generic or original to this dissertation; they are intentionally generic per the aim of developing an abstracted theoretically-focused platform characterization. Topological terminology by context Context: Abstract Real World Platform Specific Structure (○→○→○ ) Graph Network Platform Network Unit ( ○ ) Vertex Node Component Connector ( → ) Edge Tie/Link Connection/Interaction I default to platform specific terminology (i.e., “components and interactions”) throughout the dissertation, but occasionally pivot to (real world) network terminology (i.e., “nodes and ties”) when discussing more general network concepts. I do not use graph terminology in this dissertation. A variety of terminology is used throughout the platforms literature to refer to components (e.g., actors, members, users, participants, complementors, producers, etc.) and interactions (e.g., transactions, exchanges, connections, etc.) in the broad sense. I try to bridge the language used in the cited literature to its platform-specific topological terminology where relevant. xiv ACKNOWLEDGEMENTS To my committee: Danielle: Thank you for always keeping me organized and moving forward. Dave: Thank you for your careful attention to detail and expert writing advice. Gene: Thank you for your refreshing levity and uncanny ability to anticipate things. Chris: Thank you for your unwavering encouragement and incredible thoughtfulness. Marc-David: Thank you for always—always—looking out for me. Despite my academic oafishness, you stuck it through to the end. I am forever grateful for all the support you have provided me throughout these long years. Where you had every right and reason to tighten the sociological iron cage, you gave patience and understanding. I know you have supported me in ways too many to count; and more that I am not even aware of. Words cannot express my gratitude. To the incredible people at Sauder, UBC, and beyond, that have been a part of my journey: Thank you to everyone that has had to sign off on things and keep me on top of administrative matters (especially Elaine, Nancy, Sally, Sandra, Marc-David and Danielle): you've always made things as easy and smooth as possible, despite my last-minute tendencies. Thank you to my peers and colleagues for stimulating conversation and friendship (especially Marjan, Alex and Feng). Thank you to the incredibly generous scholarship and fellowship donors that supported my work throughout the years (especially the Zlotnik family). Thank you to all the mentors and instructors that have guided me throughout. I will always cherish the formative experiences and those incredibly rewarding “light bulb” moments (especially exploring the OT landscape with Martin, and spending days at the RDC analyzing data with Mahmut). To Lee: thank you for supporting me as I transition into the next chapter of my career while completing the PhD. You are a masterclass in servant leadership and emotional intelligence. To friends and family, old and new: You are always there to make the good times great, and the tough times easier. You never fail to recharge my batteries at the end of a busy week. Ba, Mẹ, Lisa, Ni, Arthur, Curtis, Susan, Jenny, Tom, Barry: thank you for constantly making the effort to be with us despite distance and convenience. You fill the weeks with vibrancy and laughter. Thank you also to all the wonderful families we met during our time at UBC and particularly Acadia Park. Being a part of such a beautiful community made a huge impact on our well-being and we are grateful for the lifelong friendships we developed along the way (especially the ever-generous Kozamara family). xv 妈妈 and 爸爸: Without you I would not have been able to take hold of this unlikely opportunity. You have kept me grounded and helped me realize the importance of not taking things for granted. Thank you for always trying to support me in the ways you know best. To Quyen: “I know plenty of people who did their PhD while raising small children—it’s perfectly reasonable!” Like moths to a flame, we charted a course to our perfectly reasonable next adventure. Over the many long years, you graciously supported me despite how perfectly unreasonable things could become. Vaguely, I would try to explain my work. Every time, you listened and encouraged me to go again. You are my rock; and the funniest—most resilient—person I know. Over all the ups and downs, you kept things afloat. Unreasonable or not, I wouldn't change a thing. To Olive and Em: Thank you for not making fun of your dad for taking so long to finally finish school! There was so much going on over these years, but I never had to compromise being your dad. The people above gave me that extraordinary privilege—without their support, it would not have been possible. I hope that you are as blessed as I have been and find yourself surrounded by mentors, friends, family, and colleagues as kind, compassionate, and generous as those wonderful people. Finally, thank you for using your magical kid powers to make me feel like the luckiest person in the world. xvi DEDICATION For Em, Olive, and Quyen 1 CHAPTER 1: INTRODUCTION Background Platforms are organizing structures that generate value, grow, and survive by scaling, managing, and exploiting network effects. Network effects refer to the positive externalities generated through the adoption and use of a good by others: the larger the network of users, the greater the value of the good (i.e., platform) to users (Katz & Shapiro, 1985). Network externality dynamics are contextually determined, and can be complex (e.g., Gupta et al., 1999). Platforms are increasingly the nexuses of value creation and economic organization (Gawer, 2009b; Van Alstyne et al., 2016). Accordingly, popular discourse on platforms has boomed over recent years (e.g., Choudary, 2015; Evans & Schmalensee, 2016; McAfee & Brynjolfsson, 2017; Moazed & Johnson, 2016; Parker et al., 2016; Srnicek, 2017; Tiwana, 2013); building on platforms’ characterization as this era’s dominant business model (e.g., Cusumano et al., 2019). Just as the corporate structure emerged from—and formed—the foundation of the industrial economy, platforms are increasingly emerging from—and propelling—the digital economy. Digital platforms continually open up new opportunities for innovators and entrepreneurs (Nambisan et al., 2019), particularly as advances in ancillary technologies ensue (e.g., Alaimo & Kallinikos, 2022; Allen et al., 2020). As such platforms develop, so too do deliberations around strategically managing stakeholders (e.g., Carrasco-Farré et al., 2022) and participants (e.g., Cenamor & Frishammar, 2021). Platforms reorganize and reform key facets of society and social life in profound, and potentially concerning, ways (e.g., Lei, 2021; Montgomery & Baglioni, 2021; Vallas & Schor, 2020). 2 Organizational theory has largely been grounded on the dominant organizational structure of its time: the firm (Coase, 1937; Cyert & March, 1963; Simon, 1991). Evidence suggests an ongoing paradigmatic transition period (cf. Astley, 1985; Schumpeter, 1942), exemplified by the decline of the corporate firm (Davis, 2016) and the rise of the networked market platform (Parker et al., 2016). As organizing structures, firms and platforms share similar aspects but also engender vast differences. As a result of organizational theory’s prior focus on firms, and not platforms, current management and organizational theory lacks precision for analyzing contemporary platform dynamics. The dominant reason for this theoretical disparity is that platforms follow a different organizational logic compared to traditional organizing structures (Van Alstyne et al., 2016). Platform coordination is technically mediated, following a market-based authentication logic as opposed to a hierarchy-based authority logic. Compared to traditional formal organizations (e.g., firms), platforms have porous boundaries to participation; yet facilitate rigid and reductive action sets while relying on authentication by a stable organizing structure. Unlike the internal authority hierarchy of traditional organizations (e.g., Weber, 1978), platform participants are external autonomous complementors1. As a result, the traditional cornerstones of organization scholarship, including those concerning strategy and design, merit reconsideration when theorizing and analyzing platform organization. Moreover, organizational theory typically casts the organizational unit as embedded in, and subjected to the forces of, a broader environmental structure. Platforms subvert—indeed, “invert” (Parker et al., 2016)—the general logic of more traditional organizational forms. Platform viability depends foremost upon effectively environing peripheral components as opposed to internal resources, and are more 1 Many digital platforms strategically develop, manage and promote their own (i.e., internal) complements (e.g., proprietary content). However, it is practically sufficient and theoretically conservative to treat complementors as external and autonomous for the purposes of this dissertation. 3 market-like than traditional hierarchies2. As a result, the theoretical angle should also be revised from environed organization to environing organization. Put another way, organizational theory should not only situate platforms in their environments as per convention, but also seek to understand how platforms operate as an environment. Research Question and Motivation As platforms increasingly organize social and economic activity, understanding platform dynamics becomes increasingly important. This dissertation’s research question, which follows naturally, is: how is platform activity organized? Surprisingly, there has been little progress in answering or even highlighting this general question. Although significant research attention has been directed towards platforms research, the majority of strategic management and organizational scholarship focuses specifically on understanding inter-platform competition; with the principle guiding question appearing closer to: how does a platform dominate its market? The extant literature answers resoundingly: by attaining the largest network. The attention to competition can be traced to the platform literature’s theoretical roots. The organizational literature on platforms is rooted in two primary research streams: (1) industrial economics (Rochet & Tirole, 2003), and (2) technology 2 It is worthwhile to reflect on the historical relationship between organizational studies and industrial economics here. In particular, the theory of the firm (Coase, 1937) and its dichotomization of the market from the firm (i.e., hierarchical organization) parallels the analytical units that center each field’s scholarly pursuits (to clarify, firms and markets are important to both communities, but the key distinction is emphatically implied; e.g., firms within markets versus markets of firms). Much of twentieth century research on economic organization explicitly defines scholarly domains according to the market and organization duality (e.g., Simon, 1991). Platforms organize markets; and therefore can be construed as a hybrid form of market and formal organization. Moreover, platforms are typically administered by traditional organizations. For instance, the strategy literature focuses on how the firm (i.e., platform sponsor) and its various strategic levers can impact the competition and innovation dynamics of its network. In general, industrial economics emphasizes horizontal (i.e., market) dynamics while technology management emphasizes vertical (i.e., innovation) dynamics. Although the complementarity between research areas is clear, the research streams remain relatively confined to their respective lanes (McIntyre & Srinivasan, 2017). 4 management (Anderson & Tushman, 1990; Henderson & Clark, 1990; Hughes, 1987). The popular platforms discourse predominantly draws from the first, newer, stream while the second stream is well-embedded (i.e., deeply integrated) in the organizational theory literature on technology and innovation. Both traditions hold strong economic assumptions around “rational self-interested actors;” which may explain underlying assumptions around platforms’ competitive dynamics being determined through network size—and the topical deference to competition in general. Extant platform theory generally predicts that a single platform will dominate a given market solely by means of securing the largest network. Because a platform’s value and appeal to participants depends on the number of other platform participants, nascent participants will join the platform with the largest network—all else being equal. This size-value axiom is distinguished as network effects (Katz & Shapiro, 1985)3, and is widely viewed as the fundamental mechanism determining platform competition (Choudary, 2015; Parker et al., 2016; Rochet & Tirole, 2003). Consequently, platform strategy is commensurate to attracting as many participants as quickly as possible (Cennamo & Santalo, 2013; Noe & Parker, 2005). Network size is the be-all and end-all. This prevailing prescription is rooted in core assumptions that recent research calls into question (e.g., Afuah, 2013; Cennamo & Santalo, 2013; Lee et al., 2006; Shankar & Bayus, 2003). Afuah (2013) synthesizes the taken-for-granted assumptions underscoring network size’s traditional treatment (p. 259): 3 Formally network externalities, as in the economics literature; “network effects” is used colloquially and throughout contemporary platforms management literature. I use network effects throughout the rest of the dissertation. 5 1. Every member of the network can transact with every other member and benefit equally from transacting with each member (Assumption 1). 2. There is resource/capabilities homogeneity across network members and across network providers (Assumption 2). 3. All network members are rational and have identical information about each other and about all possible transactions within the network (Assumption 3). 4. Information flows seamlessly from member to member (Assumption 4). Although conducive for mathematical modeling approaches (i.e., neoclassical economics), these assumptions which form the foundation of the size hypothesis—that the relationship between network size and platform value is exponential in form, and therefore, the larger network corners the market—misconstrues the reality of platform behaviour. These assumptions are invalid (for details, see Afuah, 2013); and their deficiencies serve to root and motivate this dissertation. First, real world networks are only sparsely connected (Barabási, 2016). Second, value manifests heterogeneously among (Lee et al., 2006) and within (Swann, 2002) members (i.e., components). Third, real-world platforms ultimately facilitate activity among only boundedly rational (March & Simon, 1958) actors (i.e., components); and their structural arrangements can be (dis)advantageous (Afuah, 2013; Burt, 1992). In other words, platform participants—and their resulting actions—are imperfect. As a result, networks and their members (i.e., components) acquire asymmetric dependencies (e.g., Uzzi, 1997) and—therefore—value (Rietveld et al., 2019). Fourth, transaction costs and frictions are inherent to platform participation, regardless of how technically seamless information transmits. For example, many contemporary platforms organize markets where quality is difficult to ascertain. Typically, these platforms rely on imperfect and relatively crude signalling mechanisms (e.g., reputation scores, price, etc.) to mitigate uncertainty and mismatch (e.g., Afuah, 2013). 6 Consequently, emerging platforms research increasingly exposes the deficiencies inherent in the present rational-economics rooted paradigm. For example, take several studies of the video game industry. Shankar and Bayus (2003) found that smaller, stronger, platform networks can outperform larger competitors. Cennamo and Santalo (2013) show that strategic differentiation can prevail in platform competition—contrary to the winner-take-all regime that the strategy literature largely presumes. In addition, Rietveld and Eggers (2018) find substantial evidence of demand heterogeneity effects across the platform lifecycles of the leading UK video game consoles from 2000 to 2007. Network effects are complex, manifesting asymmetrically among platform participants in ways that are contextualized by the broader platform environment as well as participants’ own social networks. The ways in which platform networks organize are highly nuanced and consequential. Afuah (2013) elaborates the implications of disregarding network structure; emphasizing that network members (i.e., components) do not connect to all other network members, even if they can. Similarly, Lee, Lee, and Lee (2006) argue that network value is localized, manifesting heterogeneously across platform participants (i.e., components) according to other participants made accessible across platform networks. Boudreau and Jeppesen (2015) find that although network growth can stimulate positive complementor development, their subsequent contributions can fail to stimulate network effects. Further research highlights the competitive contingencies (e.g., Cennamo & Santalo, 2013), complex network curation (e.g., Rietveld et al., 2019) and vertical integration-versus-augmentation (e.g., Zhu & Liu, 2018) tradeoffs facing platform sponsors; emphasizing that the implications of strategic maneuvers are highly contextualized (Cenamor & Frishammar, 2021). 7 In essence, emerging platform scholarship exposes the theoretical significance of inaccurate assumptions and overlooked features. Refuting assumptions around perfect networks, actor rationality, and feature homogeneity (e.g., of preference, interaction, capability, time, etc.) brings the validity and scope of existing perspectives into question. Consequently, I contend that platform perspectives will benefit from typological refocusing and theoretical elaboration of such features. In turn, more generalizable theoretical perspectives can emerge. Accordingly, mounting evidence suggests that network effects—and therefore, platform dominance—can no longer be inferred from, nor deferred to, network size (Afuah, 2013; Asvanund et al., 2004; Boudreau & Jeppesen, 2015; Shankar & Bayus, 2003; Suarez, 2005; Swann, 2002; Zhu & Iansiti, 2012). Platform networks’ structural aspects, alternatively, can significantly impact their subsequent dynamics and evolution (McIntyre & Srinivasan, 2017). Kretschmer, Leiponen, Schilling, and Vasudeva highlight that “the success of platforms hinges on cooperation, coordination, and integration across a diverse and often very large array of organizational units and agents” (2022). This contention interrogates contemporary platform strategy, which focuses foremost on generating network size—as quickly as possible (Cennamo & Santalo, 2013). Put plainly, structure matters immensely in real world platform dynamics; and we cannot fully understand general platform behaviour until we explicitly incorporate platforms’ network structure. Therefore, it becomes increasingly clear that critically deterministic aspects of platforms and their networks can no longer be black-boxed. That is, platform outcomes can not be inferred from network size alone4. Rather, platforms, the participants they organize, and the 4 As well, measuring network size may pose difficulties in the context of fuzzy boundaries between interoperable platforms with multiple access points. 8 resulting network structures can vary substantively. The theoretical implications of heterogeneously structured platform dynamics consisting of multiple platforms with varying participants and network organization, though largely unexplored, are essential to understanding platform dynamics. Accumulating research (e.g., Afuah, 2013; McIntyre & Subramaniam, 2009; Shankar & Bayus, 2003; Suarez, 2005; Swann, 2002; Venkatraman & Lee, 2004) directs attention towards network structure and highlights that, in order to adequately answer platform strategy questions, we must first understand the platform networks’ organizational aspects; rather than deferring to network size. It is worthwhile to note that very early organizational theory research ascribed a similar primacy to size; without detailing other mechanisms (see Hall et al., 1967; Kimberly, 1976). While the idea of organizational theory based purely around size may seem absurd given its currently rich theoretical tapestry, this is precisely the state of contemporary platforms research. Where current platforms research parallels early organizational studies research in this regard, I also hope to draw a parallel transition away from size and closer to the actual mechanisms directing platform dynamics. Given the substantial research acknowledging the limitations of current approaches (i.e., with their assumptions around network size), they remain unaddressed. A plausible explanation for the lack in response is that the limitations simply cannot be addressed with currently available frames. As such, this dissertation’s goal is advancing a theoretical framework to analyze platforms’ structural qualities, and their consequences. To develop such a framework, I focus on platform activity as the unit of analysis and central research tenet. Defining and measuring platform activity is essential to repositioning and advancing platform theory. This pivot is important for at least three reasons. 9 First, platform activity provides a general and proximal conceptualization of platform performance. Compared to the current practice of indirectly inferring platforms’ ex-ante competitive prospects from network size, platform activity directly captures ex-post platform use. Network size captures a platform’s potential for use—not its actual use—and can be misleading as platforms with smaller networks can actually organize greater activity than seemingly larger competitors. Moreover, incumbent platforms often fall into decline when their networks are at their largest (e.g., Gehl, 2012; cf. Schumpeter, 1942). As such, network size is an unreliable representation of platform performance. Ultimately, network size facilitates a broader scope and scale of latent platform possibilities; it is a means to an end. By centering analysis around platform activity, platform performance is observed at its realized end—directly capturing functionality. Second, interpreting platform activity structurally (i.e., as a network topology) provides a means to represent platforms’ network organization (i.e., characteristics and qualities); addressing a theoretical oversight in the platforms literature (Afuah, 2013; Cennamo & Santalo, 2013; McIntyre & Srinivasan, 2017; McIntyre & Subramaniam, 2009; Swann, 2002). This representation of platform organization is particularly important because of the limitations inherent in the size hypothesis (i.e., that the largest network is the most valuable to users; see Afuah, 2013). The network size axiom assumes full network connectivity (i.e., that all network components are connected to all other components). Achieving full connectivity is a far cry from the sparsely connected networks observed in reality (Barabási, 2016). Therefore, inferring platforms’ competitive prospects from network size is problematic when connectivity is presumed to scale with size; an often inaccurate assumption. Larger platform networks are not necessarily “stronger” networks. Shankar and Bayus (2003) distinguish network size from 10 network strength, “which can be viewed as the marginal impact of a unit increase in network size on demand” (p. 376), and find empirical support for heterogeneous network strength across competing platforms. Furthermore, connectivity ultimately enables platform activity. Shifting to a platform activity perspective addresses this problem by relaxing connectivity assumptions (i.e., although connectivity enables activity, it does not necessarily guarantee activity) and, instead, places platform activity—and its organization—at the fore. This is a key advancement because—although platforms research increasingly highlights the critical importance of network qualities using terminology such as network strength (Shankar & Bayus, 2003), network intensity (McIntyre & Subramaniam, 2009) and network composition (Swann, 2002)—there is no established framework formalizing these network aspects. Initializing an explicit conceptualization of platforms’ network organization provides an interface for adapting network theory—which represents structure as nodes connected by ties—to platforms research by construing activity as the ties connecting component nodes (for a review of network theory in the organizational studies, see Borgatti & Foster, 2003). Extending the network paradigm (i.e., representing structure as connected nodes) to platforms research interfaces a rich theoretical toolkit to conceptually formalize platform network organization and guide theory development on platform network dynamics more generally. More specifically, I adopt network ecology principles such as analyzing at the system (i.e., network) level and focusing explicitly on the topology of connections between components—and relating back to how their organization impacts the system as a whole5. By developing a framework to make sense of platform network organization, this dissertation also 5 I elaborate further on network ecology’s influence in Chapter 3. 11 directly responds to calls for research around the evolution of entire social organizational networks (Powell et al., 2005; Salancik, 1995). Third, pivoting to an activity-oriented approach expands the flexibility and scope of examinable platform contexts. Research leans towards an industrial economics approach describing inter-platform competition as a race to secure the largest network, generally among two otherwise identical platforms competing for market monopoly. This “two identical fledgling platforms duopoly” scenario overlooks the complexity of platform dynamics (e.g., Cennamo & Santalo, 2013; Lee et al., 2006; Shankar & Bayus, 2003). Consequently, platform management’s strategic objective and prescription is to get big—fast. Such overly general approaches can be detrimental when applied without considering the broader environmental context. In their study of the video game console market, Cennamo and Santalo (2013) found diminished strategic benefits when competitors simultaneously pursued a get big fast approach with equal intensity—potentially manifesting in detrimental performance. In addition to ascribing primacy to network size, this approach focuses on a very narrow platform topic (i.e., competition). Platforms can compete in environments with several differentiated competitors6, just as they can be positioned against a single large incumbent7. Platform and participant heterogeneity, as well as the resultant network structures that emerge, remain overlooked in extant research. For instance, what strategic prescriptions follow for platforms that are not entirely concerned with direct competition (e.g., public libraries as platforms, cultural institutions such as museums, etc.)? An activity-based framework focuses on platform functionality as performance and therefore 6 Some examples include publishing (e.g., academic), retailers (e.g., fashion/clothing), etc. 7 Some examples include search engine host, web browser, etc. depending on context (e.g., timeframe, geographic scope, etc.) 12 expands into broader platform contexts and problems beyond—but still including—inter-platform competition. Dissertation Structure This dissertation consists of six chapters. In Chapter 2, I provide a literature review on the state of platforms research. In Chapter 3, I introduce a network dynamic perspective to platforms research and develop a set of hypotheses according to the proposed framework. I describe my research method in Chapter 4 and report the results in Chapter 5. Finally, I conclude in Chapter 6 with a discussion of this dissertation’s contributions, limitations, future directions, and practical implications. Contributions This dissertation draws on network theory to conceptualize platforms’ network dynamics. In doing so, I also introduce the theoretical construct of network activity and make at least three contributions to platforms research. First, I position platform activity as the foremost variable of interest. Platforms’ network activity, referring to the activity realized through a platform, can be contrasted to platforms’ network size, which refers to the number of components accessible through the platform. Currently, network size is the default strategic imperative guiding platform management. We pay little attention to what actually occurs within these platform-networked markets8. However, emerging research suggests that network dynamics are complex, and that 8 Though I attribute the lack of attention to the theoretical black boxing of platform networks’ internal dynamics, I suspect that a large driver of this absence is also the lack of empirical opportunities; something non-trivially addressed in this dissertation. 13 greater network size does not guarantee superior network effects (Asvanund et al., 2004; Boudreau & Jeppesen, 2015; Suarez, 2005). Smaller platform networks can be more robust (Shankar & Bayus, 2003). Network value is complex, and perhaps better understood as differentially distributed amongst heterogeneous actors (Lee et al., 2006). These network size concerns are especially highlighted in the current era of platforms, which are considerably more accessible and low investment than networked technologies originally associated with the topic (e.g., Arthur, 1989; David, 1985). When contemporary platform membership is widely available and accessible, often within a few swipes of a screen, the gravity of network size merits reconsideration. In other words, when platforms are so freely accessible, what does it really mean to be a member? As such, I introduce the theoretical construct of network activity9. Therefore, this approach swaps upstream ex-ante latent performance in the form of network size for downstream ex-post actualized performance in the form of network activity. As a result, no assumptions are made around the network size and its contribution to platforms’ actual functional performance. Second, I extend network theory to conceptualize platform networks. In doing so, the activity structure of platforms’ networks can be formalized and analyzed. Research suggests that platform networks’ internal dynamics can be a key source of competitive advantage, even superseding the impact of network size. For instance, studies on the video game console industry find that size-based network effects become diminished when similarly positioned platforms employ aggressive network growth strategies (Cennamo & Santalo, 2013), while platforms with stronger—yet smaller—networks can ultimately emerge with larger market share (Shankar & 9 Network activity is multifaceted. For example, it can refer to volume of activity as well as volume of size of activity (e.g., a small transaction versus a large transaction). As this dissertation aims to introduce a highly abstracted framework for platform network analysis, activity is not differentially weighted. Incorporating differentially weighted or valued activity is discussed further in Chapter 6: Discussion and Conclusion. 14 Bayus, 2003). The general idea that platform network quality provides benefits to platforms beyond network size is expressed using terminology such as network strength (Shankar & Bayus, 2003), network intensity (McIntyre & Subramaniam, 2009), and network composition (Swann, 2002). Although network structure clearly matters, we currently lack a framework to make sense of such features. Third, this dissertation addresses mounting concerns around the appropriate unit of analysis for platforms research (de Reuver et al., 2018) by shifting the unit of analysis downstream to platform activity. The bulk of contemporary platforms research takes the platform core (e.g., platform sponsor or technological core) as its focal unit of analysis. It is perhaps due to this reason that the platforms literature has amassed such a rich volume of content around the various levers available to platform administrators. However, due to the complexities introduced by the nested, interdependent and overlapping nature of platform ecosystems (Jacobides et al., 2018), it becomes increasingly difficult to attribute causal outcomes to a single platform core independent of its broader contingencies. More recent information systems research moves the unit of analysis downstream from platform core to focus instead on platforms’ boundary resources (e.g., application programming interfaces, software development kits, etc.), which typically act as interfaces enabling complementors to innovate using the platform architecture (Ghazawneh & Henfridsson, 2013; Karhu et al., 2018). The boundary resources orientation places platform analysis closer to the source of network growth by focusing on the edges of a platform ecosystem and its evolution as a result of its upstream parameters (e.g., around design and governance). This dissertation also has the potential to make a significant practical contribution. Although platform scholars have neglected platform activity seemingly in favour of platform 15 size, the former is ubiquitous in the practice. In reality, contemporary platforms’ key performance indicators are measured in activity terms (e.g., active users, views/hits/transactions, average time spent, etc.). The approach developed throughout this dissertation can substantially bridge the “research-practice divide” that is clearly present in the platforms context; bringing theory closer to the focus of actual platform organizations. Furthermore, the tools developed in this dissertation can provide platform managers avenues to leverage their data resources to measure the organization of their activity, which can ultimately be incorporated into performance management procedures. Ultimately, this dissertation aims to develop theory more closely matching reality by removing inaccurate simplifying assumptions. Although this dissertation focuses its literature review on the industrial economics and technology management streams, it is worthwhile to note that a more recent body of information systems research espouses the importance of managing boundary resources at the interface level (e.g., Ghazawneh & Henfridsson, 2013; Karhu, Gustafsson, & Lyytinen, 2018). The view represents a downstream shift from platform level analysis. However, several limitations and concerns shroud the development of such a perspective; such as the difficulty of determining analytical boundaries and overcoming the heterogeneity and contributions of boundary resources themselves (Boudreau, 2010). This dissertation’s framework resolves these limitations. A network activity approach implicitly incorporates the effects of upstream levers manifesting at the interface level as well as providing a clear definitional boundary by constructing an analytical border around all activity made possible by the platform. These boundaries can be reduced according to predetermined vertical “layers” in a platform stack (e.g., “Wintel network activity” as activity made possible by Windows and Intel together, “LAMP network activity” as activity made possible by the Linux-Apache-MySQL-PHP software infrastructure, etc.), as explained 16 further in the next chapter. I also discuss the potential for exploring competitive and cooperative dynamics by analyzing networks with common dependencies (e.g., The PC operating system and chipset manufacturer architectures that evolved dynamically from the 1990s). Although this represents a more dynamic and proximal approach for understanding platform network growth, it still fails to directly incorporate the ultimate ends to which platform innovation matters: its use. Both units of analysis interpret the platform as a technological architecture and thus are distanced from the constellations of interactions that ultimately emerge downstream among end-users. Focusing exclusively on platforms’ supply side aspects provides an incomplete, and potentially misleading (e.g., Boudreau & Jeppesen, 2015; Song et al., 2018), interpretation of platform dynamics. Moreover, this line of research further perpetuates implicit assumptions around the outcome primacy of platform dominance. Therefore, I argue that platforms research needs to shift even further downstream in order to connect the rich inventory of strategic levers (e.g., Cusumano & Gawer, 2002) to functional ends; and that upstream configurations should be understood through their impact on platform activity. In other words, platforms scholarship (particularly from strategic management) has developed a relatively strong understanding of the available levers but has yet to venture into the realm of platforms’ mechanisms10—which unfold at the network level. Finally, this dissertation contributes to the network science literature. Progress in network research has largely been governed by data and computation bottlenecks. Comprehensive and 10 The lever and mechanism metaphors are commonplace in the organizational studies; particularly in the strategic human resource management literature. The terms are sometimes used interchangeably. However, in this dissertation they distinctly represent directly configurable actuators (e.g., via policies, procedures, etc.) which consequentially drive downstream processes not directly configurable (e.g., culture, climate, motivation, etc.), respectively. In this dissertation, platform levers refer to items such as compensation/reward policies, participant fee/cost structure, and the like. I assert that these levers drive network level mechanisms which are reflected in the ensuing network activity structure. 17 granular network data is rare. To be able to deploy network theory on complete transaction level data presents an unprecedented opportunity to develop a dynamic view of networks11; incorporating temporality and structural emergence. Whereas extant research is limited to a more static, punctuated, view of networked systems, this dissertation provides an initial attempt at a dynamic, temporal, view. Moreover, where seminal research relied primarily on between-network observations to support within-network theory (Barabási & Albert, 1999), a temporal-dynamic within-network approach can be especially illuminating. In other words, dynamic network theory—both new and old—can be accommodated via an empirically equivalent dynamic network analytical approach. Although theorizing on dynamic network emergence has been central to network science for decades, it is only relatively recently that the computational and empirical opportunities have aligned to offer the capabilities for suitable statistical analyses. In addition, due to networks’ cross-contextual universality tendencies (Barabási, 2009), it is entirely possible that the network growth dynamics featured here could guide theoretical development in other network based disciplines. This dissertation is primarily framed within the context of the strategic management literature. Platform research in strategic management is rooted in traditions: (1) technology management, and (2) industrial economics. Chapter 2 reviews the literature from these two distinct research streams. I argue that a key bottleneck in platforms research lies in the lack of explicit and coherent conceptualization of platforms. Following the literature review, I elaborate key features in which the technology management and industrial economics conceptualizations 11 In some ways, this can be viewed as a network parallel to the arguments made about dynamic textual data representation in Hannigan et al. (2019)’s recent review of topic modeling. That is, the convergence of dynamic network analyses and availability of complete transaction level data (e.g., via blockchain) can “enable scholars to take fresh approaches to theory and re-examine previously intractable problems and old questions” (p. 587). 18 diverge and converge. I then use points of convergence to formalize a general platform conceptualization. 19 CHAPTER 2: LITERATURE REVIEW Platforms Contextualized Due to their increasing pervasiveness in the organizational world, platforms are attracting attention from researchers in fields including industrial economics (Rochet & Tirole, 2003, 2006; Rysman, 2009), technology management (Gawer, 2009a), information systems (de Reuver et al., 2018), strategic management (McIntyre & Srinivasan, 2017), and beyond. Technological progress, particularly in IT, fundamentally expanded the scope of platform possibilities to coordinate activity and create value (e.g., Teece, 2018). Over the past decades, the archetypal market has transitioned from geographically and temporally bounded physical bazaars to global digital networks that organize transactions instantly. Some notable contemporary platforms (e.g., Uber, Amazon, Airbnb, eBay, Alibaba, Tiktok/Douyin, Ethereum and blockchain-based distributed applications such as Cryptokitties, etc.) are administered by a single firm (i.e., platform sponsor/administrator), many of which achieve higher market valuations—in significantly shorter timeframes—than the largest traditional firms in the same competitive domain. In just over five years since being founded, Uber surpassed the market valuations of well established automotive institutions including Ford, General Motors and Honda Motor Company (based on a December 2015 valuation at USD 68 billion; Chen, 2015). Similarly, Airbnb’s market valuation exceeded that of Marriott International, the highest valued hotel management firm (based on a June 2015 valuation at USD 24 billion; Winkler & Macmillan, 2015). For a more recent example, take the global movies and entertainment market. With USD 31.6 billion in revenue for 2022 (Mansoor, 2023), Netflix accounts for roughly a third of the entire global market (estimated at USD 95.45 billion, Grand View Research, 2023). This feat highlights the incredible pace of transition, given that Netflix only started streaming in 2007. 20 Industry analysts interpret the rise of the platform as indicative of a broader paradigm shift (e.g., ride-hailing platforms in transportation, home-rental platforms in hospitality, etc.). More recently, distributed trust technology (Seidel, 2018) implementations such as the Ethereum blockchain (Wood, 2014) continue to enable new opportunities for organizing platform-based activity—and analysis. From an organizational studies perspective, platforms are a conundrum because—while they are increasingly the dominant form for organizing social and economic activity—they contradict conventional notions of organizations. For example, firms—hierarchies which emerge due to market failure (Coase, 1937)—internalize and organize resources through legal authority (e.g., Weber, 1978). In comparison, platforms—which emerge from market opportunity (Kim & Kogut, 1996)—organize external resources through technical authentication. Traditional hierarchies improve their competitive positions through vertical integration (increasing authority) whereas platforms compete on the basis of horizontal modularity (increasing scope)12. However, platforms are increasingly central to social and economic activity, both directly as market coordinators and indirectly as determinants of firm activity—as well as broader industry ecosystem dynamics (Jacobides et al., 2018). As the trend towards organizing social and economic activities via platforms continues, explaining contemporary social organization will be increasingly dependent on understanding platforms. However, incumbent organizational theories are based on traditional hierarchies (e.g., the firm). As such, many of organizational theory’s analytical perspectives might be insufficient for platform research due to the underlying conceptualization of the organization as densely-bounded legal-authority based hierarchies that 12 A concrete example of traditional hierarchies’ increasing scope via vertical integration could be an automobile manufacturer taking control (i.e., through legal ownership) of component suppliers or dealerships whereas a platform increasing horizontal scope could be a ridesharing platform expanding its services to include food delivery, or the like. 21 appropriate and defend internal resource components, as opposed to technical-authentication based open interfaces that systematize external resource components. Platform Research Roots The exact definition and core feature(s) of platforms remain unclear. Industrial economics and technology management each emphasize different problems and focus on different features of the broader platform concept. Further, additional research streams (e.g., information systems), implement their own platform conceptualizations and establish their own research focus. Industrial economics and technology management, however, are currently the dominant two research streams—and arguably subsume or root the lesser known streams13. The volume of fragmented platform research is well-recognized; manifesting calls, and attempts, for conceptual clarification and convergence on a focused research agenda (de Reuver et al., 2018; Gawer, 2009b, 2014; McIntyre & Srinivasan, 2017). Due to their prevalence in the literature, I focus my literature review on the two primary streams (i.e., industrial economics and technology management); beginning with the former. Industrial economics: Platforms as multisided markets (MSMs) Platform competition in two-sided markets (Rochet & Tirole, 2003) is generally credited for initiating industrial economics platforms research. The seminal article casts platforms as two-sided markets, emphasizing positive network externalities arising from scale economies in 13 For example, Thomas, Autio, and Gann (2014) differentiate product family, technology system, and organizational capabilities platforms whereas others group these under a broader technological architectures category. 22 demand produced for one side as the other side grows. Research focuses on transactions and strategy, particularly around pricing and other cost-related issues such as selective subsidization (Rochet & Tirole, 2006; Weyl, 2010). This stream views platforms as market mediators that create economic value by enabling transactions between two or more interdependent “sides” of users (Armstrong, 2006; Rochet & Tirole, 2003, 2006). Positive cross-side network externalities (i.e., network effects), referring to the increase in platform value to one side as the size of another side increases, are often viewed as the basis for platform strategy. The popular discourse on so-called “multisided platforms (MSPs)” draws directly from this stream (e.g., Evans & Schmalensee, 2016; Parker et al., 2016; Van Alstyne et al., 2016). Although framing platforms as markets resonates throughout the literature, a concise (cf. Rochet & Tirole, 2006) and conventional definition remains to be established (Hagiu & Wright, 2015). Technology management: Platforms as technological architectures Unlike the industrial economics stream, the technology management stream emerges not around a common definition but, rather, convergent views on technology as a platform. Platforms are cast as architectural foundations that are leveraged (Thomas et al., 2014) in forms such as innovation (Adner, 2006; Adner & Kapoor, 2010; Yoo et al., 2012), production (Baldwin & Clark, 2000; Krishnan & Ulrich, 2001; Ulrich, 1995), and organizational knowledge (Purvis et al., 2001; Walsh & Ungson, 1991). Platforms maintain dominance through network effects that create lock-in based on dependency to the architectural foundation, which inhibits multihoming (the parallel adoption of competing platforms or standards). Here, network effects are maintained from dependency upon (i.e., unwillingness to abandon) the technological architecture and/or its constituent ecosystem (David, 1985). The dependency structure, in turn, generates a defensive 23 moat through the formation of an entrenching ecosystem comprising embedded communities, and a “portfolio of complements” (Wareham et al., 2014), around the technological foundation. Studies on technology platforms have focused on openness (Boudreau, 2010; Parker & Van Alstyne, 2018; West, 2003), timing (Schilling, 2002; Suarez & Utterback, 1995), and community effects (Wade, 1995) to understand strategies for platform adoption and survival. The technology management stream dominates management and organizations scholarship. This stream views platforms as technological architectures and thematically reflects the broader technological innovation literature in organizational theory that focuses on dominant design (Anderson & Tushman, 1990), path dependent diffusion (David, 1985; Greve & Seidel, 2015), innovation appropriability (Teece, 1986), and design rules (Baldwin & Clark, 2000). Though integral to this line of platforms research, many of organizational theory’s longstanding ideas around technology management make little explicit mention of “platforms” (some exceptions exist, e.g., Kim & Kogut, 1996; Meyer & Lehnerd, 1997). Moreover, these theories assume fixed and stable boundaries, which is counter to the nature of contemporary technology platforms (McIntyre & Srinivasan, 2017; Yoo et al., 2012). This shift is typically exemplified by contrasting traditional product platforms (e.g., those used in manufacturing industries), which rely on the administration of purposive contracts aimed at generating protective closure around innovation (e.g., Teece, 1986), to digital technology platforms, which offer greater affordance for innovation due to their characteristic openness (i.e., "the easing of restrictions on the use, development, and commercialization of a technology;" Boudreau, 2010). Such openness notably facilitates generative innovation: “a technology’s overall capacity to produce unprompted change driven by large, varied, and uncoordinated audiences” (Zittrain, 2006, p. 1980); which inherently suggests a paradigm characterized by dynamic and malleable boundaries (Yoo et al., 2012, p. 24 1399). Nevertheless, the general view of platforms as architectural foundations or building blocks (Gawer, 2009a) persists, with more recent scholarship explicitly linking the term “platform” with this conceptualization. The type of foundational building block varies. For example, management research has long focused on product platforms, defined as a “set of subsystems and interfaces that form a common structure from which a stream of derivative products can be efficiently developed and produced” (Meyer & Lehnerd, 1997). Some product platform examples include Black and Decker’s power tool platform (Meyer & Utterback, 1993) and Hewlett Packard’s Desktjet printer platform (Meyer & Lehnerd, 1997). Research on industry platforms (Gawer & Cusumano, 2014), such as the Windows and Intel “Wintel” software-and-hardware architectural foundation that dominated the personal computing industry (e.g., Cusumano et al., 2019), is also prevalent. Towards a Generalized Conceptualization The two streams have notable differences and similarities. Moreover, efforts around conceptual convergence have recently been accumulating (Baldwin & Woodard, 2009; de Reuver et al., 2018; Gawer, 2014; McIntyre & Srinivasan, 2017; Thomas et al., 2014). While recognizing and anchoring on comparisons of the two platform streams, I develop an assessment with a different literary interpretation and approach to conceptualizing platforms. Identification and comparisons of the streams generally converge on similar conclusions. Although recent reviews clearly recognize the industrial economics perspective, some view the non-market (i.e., technological architectures) conceptualization as partitioned into more distinct perspectives (e.g., Baldwin & Woodard, 2009; McIntyre & Srinivasan, 2017). Nevertheless, the latter (set of) stream(s) resoundingly views platforms as technological architectures. 25 A clear formalization of the platform concept is needed in order to advance an enduring platforms research agenda. However, I argue that the definitional challenge is embedded within a larger typological entanglement requiring clarification. The technological architectures conceptualization emerged in the previous century from the technology management research stream, and is largely centered around industrial production and innovation (Gawer, 2014). In comparison, the MSP conceptualization better fits contemporary notions of the platform as a business model and is the primary basis for current popular discourse on platforms (e.g., Choudary, 2015; Parker et al., 2016). However, MSPs originated from analyses of two-sided markets (Rochet & Tirole, 2003), and not platforms per se. This is point is non-trivial. It is worthwhile to emphasize here that neither perspective originated as a theoretical lens through which to study the—primarily digital—platforms that are the interest of contemporary business discourse. In short, platform scholars are using retrofitted perspectives to study contemporary platforms. As a result, the literature continues to negotiate the definitional boundaries of the platform concept. For example, recent works have formalized MSPs’ sides to users exclusively (Weyl, 2010) and direct interactions (Hagiu & Wright, 2015), while other works are suggestive that multi-sidedness is not a determining platform feature (Hagiu, 2007; Rysman, 2009). I contend that both streams are largely imprinted (i.e., influenced) by the platforms of their time, and that definitional convergence requires consideration of typological divergence in order to establish the relevant scope conditions of the platform conceptualization—rather, platform conceptualizations. Many platform examples disproportionately fit one conceptualization (e.g., ride hailing as MSP, a motherboard standard as technological architecture, etc.) while others fit both (e.g., operating systems, which support software applications that are interacted with by users), to varying degrees. In addition to the common 26 features identified in the platforms literature, it remains unclear what features dictate the theoretical and analytical boundaries between platform conceptualizations. The lack of explicit articulation highlighting the differentiated conceptualizations between literary streams—and the potential for overlap—maintains an ambiguous border between economists that study MSPs and organizational theorists that study technological architectures. When these conceptualizations are made overt, the degrees to which platforms can incorporate aspects of both features can also enter the conversation; and hopefully enable fruitful theoretical triangulation across perspectives. The remainder of this chapter elaborates a generalized platform definition by clarifying the points of conceptional divergence and convergence across industrial economics and technology management perspectives. For convenience, Table 2-1 outlines a concise summary of the platform literature. Table 2-1: Platform Literature Summary References Stream Relevant Points Rochet & Tirole (2003) Industrial Economics -foundational paper for the Industrial Economics perspective -presents platforms as multisided markets (MSMs) -assumes perfect efficiency and homogeneity -price-deterministic competition dynamics Katz & Shapiro (1985) Industrial Economics -foundational introduction to demand-side network effects: “utility that a user derives from consumption of the good increases with the number of other agents consuming the good” (p. 424) 27 Arthur (1989) David (1985) Technology Management14 -foundational introduction to network effects as a key underpinning of technological lock-in (i.e., dominant design) -lock-in dynamics underpin “winner-take-all” assumptions Gawer (2009b) Technology Management -collection of thirteen papers exemplifying technology management perspective -presents platforms as technological architectures Afuah (2013) Cennamo & Santalo (2013) Lee, Lee & Lee (2006) Shankar & Bayus (2003) Suarez (2005) Strategic Management (primarily) -supports heterogeneity in platforms, components, and networks -disputes conventional notions of network effects -argues that network effects are not all about size -highlights that network effects are complex -challenges “winner-take-all” hypothesis that platform with largest network will corner market McIntyre & Srinivasan (2017) Strategic Management -exemplary review summarizing research fields, synthesizing key themes, and offering future directions -calls for greater integration across fields Before developing my framework for platform analysis, I clarify my definition of a platform. I elaborate and conceptualize platforms according to five interrelated features prominent in the literature: (1) structural definition, (2) component function, (3) platform function, (4) competitive logic, and (5) strategic emphasis. These five features define the typological boundaries between the two dominant platform conceptualizations (i.e., MSPs and technological architectures). Identifying the edges of typological divergence helps to not only distinguish between research streams, but also to form a mediated generalization of the broader platform concept. 14 Although these papers are foundational to the technology management literature, they actually originate from economics. 28 To guide this dissertation’s conceptualization, I aim to reveal generalized platform features common to industrial economics and technology management. Defining a generalized platform conceptualization can provide a suitable basis to develop theory supporting analysis of platforms in their capacity to coordinate markets as well as facilitate innovation. Developing theory that recognizes both of these platform functions is important because most contemporary platforms of interest generate value as infrastructures as well as markets (Choudary, 2015). To proceed, I draw attention to the typological fault-lines between “market platforms” and “technology platforms” by elaborating on how the two conceptualizations diverge and converge along each of the five features; and identifying a more generalized conceptualization for them. Structural definition While industrial economics presents platforms as multisided markets (Rochet & Tirole, 2003), the technology management stream frames platforms as architectural foundations determining (and constraining) the subsequent design and production of successive subsystems that inherit (and conform to) its relevant architectural features (Baldwin & Clark, 2000; Ulrich, 1995). Market platforms structure interactions between components whereas technology platforms structure innovation on top of the platform itself. A generalized definition leaves the form of component connection open; incorporating both component interactions and innovations. However, components do not stochastically select into and become systematized by platforms. Rather, there is coherence in components and their emergent connections. When generalized as a structure that supports both component interaction and innovation, in ways that are coherently systematized, platforms can be viewed as agglomerative ecosystems. 29 Agglomeration refers broadly to the concentration of activity, and can generate positive externalities. Rooted in economics, and urban economics in particular (Fujita & Thisse, 2013; Marshall, 1920), agglomeration describes the economies arising from intra-industry spatial concentration (e.g., Silicon Valley for tech, Milan for fashion, Shenzhen for manufacturing, etc.). Regardless of their components’ focal function (i.e., interaction versus innovation), platforms essentially agglomerate components (e.g., YouTube for videos and viewers, GitHub for code and developers, The App Store for applications and users, etc.) and organize in ways systematized by the platform and its context. Therefore, an initial structural definition is that platforms agglomerate and systematize component organization (including both innovation and interaction). Such a definition accommodates platforms’ conceptualizations as multisided markets or technological foundations. Component function Both streams have studied platforms composed of single (e.g., user-user) or multiple (e.g., user-product) types of “peripheral components” (Baldwin & Woodard, 2009; McIntyre & Srinivasan, 2017). Hence, in this dissertation I abstract platform constituents—users and their representations, complement(or)s, and other participants or participant innovations—as components15. A MSP is generally presented as a single extant structure that supports the market interactions of its components (e.g., different groups of interacting users). Technological architectures provide infrastructure for component innovation. A technological architecture 15 A component is, abstractly, something that is systematized by the platform. Components are contextual to the platform. They generally take the form of complements which are the basis of a platform’s value to users (e.g., software compatible with a particular operating system). The technology management literature differentiates between platforms’ core components and peripheral components (Gawer, 2014). For parsimony, this dissertation’s use of “components” will refer to platforms’ peripheral components since the core is not a primary theoretical focus. 30 diffuses and evolves through innovation, but can also exhibit market qualities, leading to the emergence and proliferation of complex ecosystems (Jacobides et al., 2018). For example, software act as components accessed on a given operating system (i.e., MSP view), but are also developed or deployed on top of the system’s architecture (i.e., technological architecture view). I posit that component innovation (e.g., updating a wiki, publishing software, listing a good or service, etc.) and interaction (e.g., reading a wiki, executing a software function, buying/renting a marketplace good or service, etc.) are distinct, but interdependent, forms of platform activity. Platform activity can be decomposed and abstracted by interpreting component innovation as first order connection (i.e., component to platform) and component interaction as second order connection (i.e., component to component). Both activities are platform mediated. Although component connection typology remains to be adequately acknowledged in the platforms literature, unveiling platform interaction and innovation as distinct forms of platform activity provides an important component function generalization. Platform function Platforms enable and constrain components to function in specific ways. These functions can be categorized as either innovation or interaction. Industrial economics focuses on the interaction mediating aspects of platforms whereas technology management views the platform as an innovation architecture. However, both aspects can be present to various degrees, particularly in the context of contemporary digital platforms. Choudary (2015)’s platform stack framework suggests that digital platforms consist of a market layer and an infrastructure layer. A data layer completes the three-layer stack model, but is viewed primarily as a complementary 31 resource used for improving platform value creation (e.g., by reducing search costs, improving curation, etc.). Platforms are configured according to these layers. One layer can play a dominant role over others—and configurations can evolve. The stack framework differs from the conceptualizations permeating the academic literature in that it emphasizes that multiple layers play a role—especially when platforms scale—even if one is particularly dominant. Whether value creation is primarily attributed to enabling market interactions between groups (i.e., MSP) or the innovation and production of component subsystems (i.e., technological architecture), the platform acts as a nexus of organization by systematizing components. Therefore, the generalized primary function of platforms can be viewed as component systematization. Competitive logic A similar generality can be applied to the externalities accompanying platforms’ network size, which underlie platform competition. Platform competition is determined by network effects. Network effects are construed as network size-based economies from the platform’s perspective. However, the two platform literature streams emphasize distinct economies (Gawer, 2014). Industrial economics places competitive primacy on demand-side scale economies (i.e., the volume of users) whereas technology management focuses on supply-side scope economies (i.e., the variety of complements). Economies of scale and scope can emerge as platforms’ components increase in volume and variety, respectively. Depending on the context, both forms of network economies can be present and advantageous to various degrees. The dynamics surrounding which network effects manifest and create value may well not be as definitive as the literature suggests. For instance, although economics scholars resoundingly emphasize demand-side scale economies (e.g., Eisenmann et al., 2011), Gawer (2014) takes the position that it is 32 actually demand-side scope economies that constitute the indirect network effects driving platform value. Because both types of economies can manifest to various degrees (i.e., they are not mutually exclusive), platforms’ network size-based economies may benefit from a more generalized and flexible classification. Although network effects are often equated with network size (i.e., through cross-side network effects for MSPs, and combinatorial/innovative scope for technological architectures), network benefits will only accrue to the extent that components are effectively organized. Platform components do not stochastically interact nor do they fully self-organize. Without effective agglomeration of components, platforms’ network size can very well manifest diseconomies from scale through increasing noise (e.g., in the form of search costs). For instance, the mid 1980s 8-bit video game console crash and demise of Atari—the incumbent platform at the time—remains attributed to the lack of quality curation around the many new titles (i.e., components) rapidly released (Kent, 2001). In other words, there was no mechanism to help match users to higher quality, or better suited, titles; thereby diminishing the overall experience of the platform itself. Atari suffered from a failure of effective organization. Regardless of whether platform scaling dynamics are associated with scale economies or scope economies (or both), it is ultimately the discriminant agglomeration (i.e., selective grouping) of components that create value from platform networks. For example, take Google search’s rise to dominance over incumbent search engines (Vise & Malseed, 2005). All internet search platforms have access to essentially the same components (e.g., websites), but it was ultimately Google’s superior agglomeration of the components (i.e., high search-result relevance) that created greater value to users; who, in turn, increased their use of the Google search platform over alternatives. As digital platforms scale, data is increasingly crucial to delivering platform value by improving 33 curation and relevance (Alaimo & Kallinikos, 2022; Choudary, 2015). Consequently, agglomeration economies—the benefits arising from effectively concentrating complementary activity—provide the basis for competitively generating and appropriating network effects in often taken-for-granted ways (e.g., through recommender algorithms and search features). In other words, it is not merely scale nor scope that give networks their value; but rather the discerning localization of relevant components and—in turn—their resulting connections. Although the platforms literature places heavy emphasis on competition, perhaps more important than elaborating a generalized competitive logic is building a conversation on the role of a cooperative logic. Though relatively de-emphasized in the strategic literature, streams such as information systems do tend to adopt a more cooperative framing (e.g., Ceccagnoli et al., 2012). Ultimately, the platforms achieve competitive fitness through value co-creation with components. Therefore, a more apt feature label here would perhaps be value creation logic. Strategic emphasis Platforms achieve competitive dominance by exploiting network effects. Network effects are the primary strategic determinant governing platform competition. However, the two streams have distinct emphases on the forms and manifestations of network effects. Industrial economics focuses primarily on user-based indirect network effects (e.g., Hagiu & Wright, 2015) whereas the technological architecture stream emphasizes complementarity-based network effects more broadly (Farrell & Klemperer, 2007; Tanriverdi & Lee, 2008). Indirect network effects manifest when the perceived value of a platform increases to (nascent) users as a function of complementary components, or when the value of the platform increases to (nascent) 34 complementors (i.e., complement suppliers) as the number of users increases (Hagiu & Wright, 2015). Direct network effects develop when the value of a platform increases as the number of participants from the same “side” (users to users, complementors to complementors) adopt the platform (Katz & Shapiro, 1985). While industrial economics emphasizes user sides, focusing on value created through indirect network effects, technological architectures emphasize complementary components accessed through—or integrated with—the platform. The resulting strategic mechanisms are different (Parker & Van Alstyne, 2005). MSPs exploit positive network feedback between user sides to rapidly scale value and adoption (Gawer, 2014). Technological architectures, on the other hand, lock in an installed user base dependent upon a technological standard of which the platform is a critical component or even its foundation (Arthur, 1989). While the former grows through positive attraction, the latter persists through negative detraction—or, “excess inertia” (Farrell & Saloner, 1985). Platform industries are traditionally characterized as “winner-take-all” markets (Arthur, 1989; Shapiro & Varian, 1998). Industrial economics’ emphasis on sides is exemplified by the “chicken and egg” dilemma—that the platform is not attractive to a particular user “side” until the platform offers a significantly large base of components from the other “side” which the first seeks to interact with (Rochet & Tirole, 2003). Therefore, the literature emphasizes pricing strategy and selective subsidization of users to initiate cross-side network effects, (i.e., creating value for component side(s) by populating another component side) thereby establishing a large enough user base such that new users preferentially attach to the platform over less established alternatives. Technological architectures, by contrast, persist as a result of lock-in or architectural dependency. Defenses arise directly when not using the platform is costly, and also indirectly when the platform is integral to a broader ecosystem (e.g., integrated with a set of 35 complementary components) that is costly to repudiate. Moreover, these defenses are consolidated via positive feedback between platform adoption and improvement (Arthur, 1989). Hence, MSPs emphasize demand side economies of scale (increasing efficiencies from volume; Katz & Shapiro, 1985) while technological architectures emphasize supply side economies of scope (increasing efficiencies from variety; Panzar & Willig, 1981). Therefore, after they have been engineered (i.e., designed with rules, policies and protocols), network scaling is typically presented as platforms’ primary challenge. The MSP literature’s chicken and egg problem (Caillaud & Jullien, 2003; Rochet & Tirole, 2003) and technological architecture’s installed base race (Farrell & Saloner, 1986; Suarez, 2004) are subsets of a grander network scaling problem. Both challenges concern the initialization of a platform’s network in order to generate network effects. The economics literature emphasizes selective subsidization and pricing as a means of scaling through cross-side network effects (Eisenmann et al., 2006) while the technology management stream further highlights indirect network effects manifesting lock-in and scope-based defenses through ecosystem embeddedness (Farrell & Klemperer, 2007). For example, scientific communities adopt different software and modeling approaches, not as a result of an optimized search of options but rather due to compounding influences from their embedding social system (Centola & Macy, 2007; Joppa et al., 2013). The path dependent diffusion and maintenance of such norms follows the very network-based mechanisms explaining the prevalence of the inefficient QWERTY keyboard standard (David, 1985). The platform network can accelerate further adoption as well as bolster defensive aspects (i.e., lock-in) emerging from platform dependence. Both strategic mechanisms can be present to various degrees. These network effects are first cultivated from network scale because platforms are unable to viably generate value from their designated functions until 36 enough components are available. However, network scaling’s effectiveness may well be bounded (Swann, 2002), with platform competition being increasingly determined by their networks’ qualitative aspects (Afuah, 2013; Shankar & Bayus, 2003). Network dynamics can manifest heterogeneously (Lee et al., 2006), and in complex ways that remain to be adequately understood (Cennamo & Santalo, 2013; McIntyre & Srinivasan, 2017). Therefore, platform strategy revolves around a broader network management challenge, which encapsulates the complex quantitative (i.e., scaling) and lesser understood organizational aspects of network effects. Technological architectures and MSPs converge on many core aspects. I encapsulate these characteristics in a mediated organizational platform conceptualization, and contrast them against conceptualizations of the two dominant platform research streams, in Table 2-2. Table 2-2: Comparison of Platform Conceptualizations Market platforms Technology platforms Generalized conceptualization Structural definition Multisided market Architectural foundation Agglomerative ecosystem Component function Interaction Innovation Activity Platform function Interaction mediation Innovation infrastructure Component systematization Competitive logic Demand-side scale economies Supply-side scope economies Agglomeration economies Strategic emphasis Scale-based: Pricing / Subsidization Network growth Defense-based: Lock-in / Dependence Ecosystem moat Network-based: Network management Network effects 37 Definition A platform can generally be defined as an entity that systematizes components through authentication. This dissertation abstracts any object or entity systemized—and therefore, authenticated—by the platform as a component. To systematize is to “organize something according to a particular system” ("Systematize," n.d.). A system is “a set of connected things or devices that operate together” ("System," n.d.). Authentication refers to “an act, process, or method of showing something (such as an identity, a piece of art, or a financial transaction) to be real, true, or genuine” ("Authentication," n.d.). Though platforms typically revolve around facilitating a highly specific function, components and their connections are authenticated in myriad ways. Usually, however, authentication derives from design and functional constraints. Constraints can authenticate components at the platform interface, as well as during attempts to connect with other components. For example, digital platforms often require credential validation (e.g., user login, licenses, etc.) before users can access platform features. Similarly, physical interfaces can restrict components through form adherence requirements (e.g., mounting patterns and dimensions, socket standards, etc.). Platform interfaces generally determine which components are eligible for connecting to the platform. Functional constraints at the platform level restrict—yet also define—the connections that components can generate. Similarly, technical constraints on the component side such as code adherence (e.g., syntax in languages, operational knowledge, etc.) further limit the capacity for interaction. It is precisely because platforms organize around a strictly defined core interaction that analyzing an activity-based network topology becomes justifiable. In contrast, conventional bureaucratic systems arrange an immeasurable variety of interactions that are therefore not conducive to equilateral treatment. 38 Any platform perspective inherently draws analytical boundaries based on organizational form by focusing its theoretical scope on platform organization, and excluding alternative organizational forms. The two dominant platform perspectives draw further analytical boundaries according to conceptualization: MSMs that systematize interactions versus architectural foundations that systematize innovation. While the industrial economics perspective suits platform-mediated markets, its theoretical utility likely decays as technology aspects increasingly dominate platform dynamics. In contrast, technology management’s analytical suitability likely decays as market aspects dominate. Although some technology platforms may not explicitly orchestrate component matchmaking, market dynamics can emerge. Therefore, relying solely on a market or technology perspective to analyze contemporary platform dynamics is particularly concerning because most digital platforms must balance both innovation and interaction; even if one aspect appears to dominate at one particular point in time (e.g., Choudary, 2015). Construed as either MSM or technological architecture, platform scholarship risks overlooking—and inappropriately inferring (e.g., Afuah, 2013)—the emergent complexities of component interaction, innovation, and their intersectionality. Particularly in the context of contemporary digital platforms, it is difficult to identify a platform that can be construed as a “pure-type” technological architecture or multisided market. It is only relatively recently that clear and succinct definitions around digital platforms are emerging. According to Saadatmand, Lindgren, and Schultze (2019): “digital platforms are an organizational form made up of a technological architecture and governance mechanisms for managing autonomous complementors” (p. 1). Even still, the definition remains clearly anchored in the technology management tradition. 39 Conceptual Boundaries The platform concept has coherence across research streams, but also nuanced differences. Industrial economics studies platforms as markets involving multiple interacting sides while technology management studies platforms as foundational building blocks governing innovation and production. However, most contemporary digital platforms generate value through innovation as well as interaction (Choudary, 2015). For example, operating system platforms such as those found in video gaming and personal computing can be viewed appropriately as MSPs (e.g., Rysman, 2009) as well as technological architectures (e.g., Langlois & Robertson, 1992; Teece, 1986). Contemporary digital platforms are typically developed upon multiple successive technologies (e.g., de Reuver et al., 2018; Yoo et al., 2010). Sequentially stepping through platform dependencies expands a chain of “layers”16 which represent a platform’s underlying architecture—or technology “stack.” The gamut of technology management literature represents platform ecosystems in such infrastructural (i.e., vertical) “depth” terms. Conversely, the industrial economics literature emphasizes platforms’ interaction-based (i.e., horizontal) market “breadth.” A cross-section along platforms’ infrastructural (i.e., innovation) connections is analogous to an architectural view (i.e., technology management) whereas a cross-section of platforms’ component interactions corresponds to a market view (i.e., industrial economics). 16 The “layer” terminology’s use differs between Choudary’s (2015) platform stack framework and the technology stack framework. Whereas the latter refers to the technologies that constitute a platform’s underlying architecture—and are generally platforms themselves—the former refers to the three layers of value creation (market, infrastructure, and data) for analyzing platform business models. For example, YouTube’s technology stack consists of several infrastructure layers (i.e., technologies) including the Apache server, MySQL database, Python programming language, and Linux operating system. YouTube can also be represented as a business model that generates value through its market, infrastructure, and data (Choudary, 2015). 40 Although the industrial economics and technology management streams attain conceptual convergence on several key aspects, divergent elements that define the boundaries of each perspective also exist. The primary boundary separating the two dominant platform research streams is the form of component connection constituting platform activity. Technological architectures highlight component-to-platform activity (i.e., innovation) whereas MSPs emphasize component-to-component activity (i.e., interaction). The fact that modern market organizing platforms (i.e., those directly facilitating component-to-component interactions) are developed upon technological building blocks can be a potential source of distortion, particularly when platforms are not clearly conceptualized. Regardless, even platforms that are conventionally conceptualized as technological architectures evolve through market dynamics (e.g., Cennamo & Santalo, 2013; Gawer, 2014). Therefore, it is not particularly surprising that inter-platform competition aspects are primarily framed according to the industrial economic lens (Gawer, 2014). Technology Management Emphases Organizational theory is foundational to the technology management stream. Active research within the stream contextualizes platform dynamics within industry ecosystems (e.g., see Nambisan, 2018). Industry ecosystems are analogous to the complex of entities (e.g., firms) and their technological constituents (e.g., platforms) representing the assortment of platform “stacks” that are connected through value creating interdependencies (Jacobides et al., 2018). Platforms’ competitive dynamics manifest across and within ecosystems as a value creation versus value capture problem (Jacobides et al., 2018, p. 2268). Within ecosystems, a platform “stack” can be conceptualized as a vertical “value path” (Henfridsson et al., 2018) that 41 cooperates to create value, yet competes to capture value. This coopetition emerges within an ecosystem because participants create value interdependently yet capture value asymmetrically due to asymmetrical dependencies (Jacobides et al., 2006; see also Pfeffer & Salancik, 1978). The “bottleneck” segment of the stack (i.e., “the assets that are in high demand but are not competitively supplied”; Teece, 2018) acquires an architectural advantage by means of such dependency asymmetry, and consequent power to shape the ecosystem (Jacobides et al., 2006)—and its competitive course (i.e., inter-ecosystem competition). In the technology management stream, platforms are strategically concerned with how to manage dependencies within ecosystems in order to elevate their structural power (cf. Pfeffer & Salancik, 1978) and—consequently—appropriate and capture ecosystem value (Jacobides et al., 2006). Platforms are contextualized “vertically” as constituents of these larger ecosystems. While this perspective is suited to address questions about the vertical dynamics (i.e., innovation; e.g., Adner & Kapoor, 2010) within a platform stack, it remains limited in its ability to analyze more direct forms of inter-platform competition (e.g., for structurally similar positions within ecosystems). Casting competition to the industry ecosystem level limits the perspective’s strategic appropriability to those that have sufficient architectural advantage to shape their industry ecosystems. Few platforms even achieve the opportunity to maintain such a leadership position due to industry ecosystems’ constant contestation (Gawer & Cusumano, 2014). However, platforms do have access to strategic levers that influence their immediate ecosystem (i.e., component network). In particular, research within the technology management stream also focuses on how platforms use such levers to attract third party complementors to their immediate network (McIntyre & Srinivasan, 2017). The information systems community is also active in addressing the complementor attraction question from the perspective of boundary 42 resources, which improve the interface (e.g., for innovation) between third party complementors and the platform (e.g., Eaton et al., 2015; Ghazawneh & Henfridsson, 2013; Karhu et al., 2018). The remaining bulk of research on complementor attraction draws heavily from the industrial economics perspective (e.g., Boudreau, 2010; Eisenmann et al., 2009; Gupta et al., 1999). Industrial economics’ influence on complementor attraction is not particularly surprising due to the fact that the research stream focuses primarily on inter-platform competition as determined by network adoption dynamics (e.g., Katz & Shapiro, 1994). In contrast to the “vertical” angle taken in technology management, industrial economics contextualizes platforms and their ecosystems “laterally.” Industrial Economics Emphases However, industrial economics concedes theoretical scope for definitional focus by casting platforms as MSMs. That is, industrial economics clearly defines its “platform problem” but relinquishes generalizability and analytical depth due to its strict implicit assumptions (Afuah, 2013; Gawer, 2014). Specifically, the MSM view conceptually reduces and homogenizes components to price sensitive “sides” thereby relinquishing any theoretical insights contingent upon the activity occurring on, and outside, the platform’s component network. Research on interaction-oriented platforms has been pursued through an economic lens insofar as the totality of interaction-oriented platforms remain generalized as MSPs. Presently, the MSP label risks being understood categorically where it should be taken as perspective. Confounding category for perspective sustains an imperceptible moat obstructing the entry of alternative theoretical approaches in the study of interaction-oriented platforms. Once acknowledged, the remedy is simple: interpret MSPs the way they were originally framed—as a multisided market 43 (MSM) view of platforms (cf. Rochet & Tirole, 2003). Distinguishing platforms on the basis of their systematized component connections (i.e., innovation versus interaction) and decoupling category from perspective may clear an opening for future theoretical innovation in platforms research. As with traditional formal organizations typically examined in the organizational studies (e.g., firms), interaction-oriented platforms are multifaceted entities. However, the MSM perspective is currently the only cohesive perspective available to study them through. The MSM perspective reduces a platform network to at least two “sides,” assuming stable equilibria determined via price setting, and homogeneity of users within each side. Such a perspective overlooks several crucial platform properties. First, network size is ascribed primacy, and the network of interactions that define these platforms are theoretically ignored. Second, the MSM perspective is limited to platforms that are multisided and have a pricing component for at least one side. Many platforms do not have a price component (e.g., particularly in early stages, when the platform sponsor incurs costs in order develop the platform network), nor do all platforms consist of multiple sides. Platforms systematising dyadic interactions readily fit the multi-sided conceptualization. However, community-based interaction platforms (e.g., Slack, GitHub, Meetup, etc.) are more difficult to conceptualize in terms of sides. In such contexts, many cited examples address this by declaring the second side to be "advertisers" even though advertisements only act as a mechanism for the platform sponsor to capture economic value from the platform network rather than generate value from platform interaction. In actuality, advertiser dependent platforms are generally community-based platforms where the network effects manifest along a singular “side” (i.e., users) and only unidirectionally across one side to the other (i.e., from users to advertisers, not vice versa—and 44 perhaps even negatively from advertisers to users). Many platform markets are also one-sided. Examples of one-sided markets include betting markets, online gaming networks, and markets where the sides overlap completely (e.g., instant messaging, social networks, etc.). Moreover, the gamut of MSP theory is developed from two-sided markets. However, the generalizability of two-sided platform theory to that of multi-sided platforms is questionable as additional sides may well be accompanied with nonlinear (i.e., complex) changes to network dynamics. While many interaction-oriented platforms can indeed be construed as multisided markets, multisidedness is not a defining feature of platforms. The MSP conceptualization facilitates the theoretical leveraging of neoclassical economics (i.e., demand-supply dynamics) but overlooks and potentially limits the development of other theoretical angles. Third, platforms are characteristically dynamic; and yet, the MSM perspective fails to incorporate this fundamental characteristic. By assuming stable equilibrium states, the MSM perspective overlooks the significance of platforms’ external dynamics. Viewing platforms as stable closed systems dismisses platforms’ environmental conditions, including the presence of competitors. Further concerns arise from framing inter-platform competition as a race to securing the largest network, generally among two otherwise identical platforms competing for market monopoly. This framing of inter-platform competition is typical of industrial economics models. However, the “two identical fledgling platforms duopoly” scenario is only one of many contexts that platforms may face. Platforms can compete in environments with several differentiated competitors just as they can be positioned against a single large incumbent. Timing can play a critical role in determining competitive outcomes (Schilling, 2002). Platforms can also leverage strategic positioning and differentiation (Cennamo & Santalo, 2013). Moreover, platform contexts can evolve in dynamic and complex ways: not only as a result of shifts in the external 45 environment, but also due to changes in platforms’ own characteristics (e.g., network size, network structure, policies and protocols, etc.). Yet, these concerns remain unincorporated into the MSM perspective. The Role of Networks Increasing efforts to integrate the streams offer clarity around convergent aspects and contribute to forming a more general platform conceptualization (Baldwin & Woodard, 2009; de Reuver et al., 2018; Gawer, 2014; McIntyre & Srinivasan, 2017; Thomas et al., 2014). There has been a generally increasing shift towards a more “lateral” view of platform competition within the technology management literature, with more recent reviews framing the overall stream as being integrated with competition aspects of the industrial economics literature (e.g., Gawer, 2014; McIntyre & Srinivasan, 2017). However, integrating concepts across platform research streams can carry significant risks. When platform typology isn’t explicitly formalized, assumptions original to one platform type may be erroneously applied to another due to the fact that many key concepts share the same label but engender nuanced yet divergent impacts on platform dynamics. For example, network effects are central to both of the dominant platform research streams. However, network effects manifest in nuanced ways. On one hand, network effects can emerge as technological dependencies embed components—and their subscribers—to a particular platform (e.g., Arthur, 1989; David, 1985). On the other hand, network effects can also refer to the positive feedback between platform adoption and platform value (Katz & Shapiro, 1985). The former builds a detraction-mitigating moat whereas the latter exponentially generates 46 momentum for network attraction. An attractive network is not necessarily sticky; just as a highly locked-in network is not necessarily attractive. Industrial economics elaborates further on network effects, focusing particularly on indirect network effects (Rochet & Tirole, 2006). However, both indirect and direct network effects can vary dynamically and interdependently (Parker & Van Alstyne, 2005). Moreover, localized network effects can manifest heterogeneously at the component level (Lee et al., 2006); and can evolve in complex ways (i.e., nonlinearly) that remain to be fully understood (e.g., Swann, 2002). Larger networks do not imply stronger networks (Shankar & Bayus, 2003). In some cases, network effects may not develop at all (Boudreau & Jeppesen, 2015). Although the literature increasingly highlights that network effects are complex, dynamic, and multifaceted, current platform perspectives still black box this centrally deterministic concept. Moreover, although current platform perspectives heavily emphasize the role of networks, their dynamics are only incorporated implicitly; or indirectly inferred. A black boxed approach to platform networks and their externalities (i.e., network effects) overlooks nuances that are critically important to understanding their inherent complexities (Afuah, 2013; Lee et al., 2006; Parker & Van Alstyne, 2005; Shankar & Bayus, 2003; Swann, 2002). In their review, McIntyre and Srinivasan (2017) highlight that “there is relatively little understanding of platform dynamics and their evolution, with platforms being treated as systems that remain relatively stable over time” (2017, p. 151). If platforms evolve, survive, and thrive on the basis of their networks, then theory should explicitly focus on platform network dynamics. By focusing on platforms’ network level dynamics, we may get closer to understanding how inter-platform competition and cooperation unfolds and—consequently—how platform activity evolves. This dissertation responds directly to such calls, making key theoretical advances by presenting a 47 dynamic, activity-oriented approach to platform network analysis. In doing so, this dissertation shifts the basis of platforms competition research from stable equilibrium-approaching size-inferred network effects to dynamically-evolving empirically-observable network effectiveness. In Chapter 3, I develop a network level approach that explicitly incorporates platforms’ internal dynamics (i.e., network structure) to understand inter-platform competition and cooperation. The proposed theoretical framework incorporates three heterogeneities that are increasingly identified as being theoretically critical yet overlooked—or inappropriately inferred—in the extant literature. First, platforms themselves are heterogeneous and situate in dynamic environments with heterogeneous competitors that impact competitive dynamics (e.g., Cennamo & Santalo, 2013; Shankar & Bayus, 2003). Second, platform components are heterogeneous and participants (i.e., complementors, users, etc.) therefore appropriate differential benefits from platform networks (e.g., Lee et al., 2006). Third, and consequently, network activity manifests incompletely and non-randomly (e.g., Afuah, 2013). The heterogeneity in platform networks’ emergent activity provides a basis for explicitly conceptualizing and measuring platform networks’ influential organizational aspects which have been suggested at using terminology such as network strength (Shankar & Bayus, 2003), intensity (McIntyre & Subramaniam, 2009), and composition (Swann, 2002). Explicitly including platforms’ network structure provides a solution to the increasingly criticized approach of inferring network effects from network size (Afuah, 2013) or ex post empirically (e.g., Boudreau & Jeppesen, 2015; Shankar & Bayus, 2003). By incorporating heterogeneity in platforms, components, and the emergent organization of platform-mediated activity, future platforms research can explicitly conceive the relative influence of networks rather than 48 implicitly assume the absolute existence of universal network effects (for a review of this thematic shift's importance and implications, see McIntyre & Srinivasan, 2017, p. 152). 49 CHAPTER 3: THEORETICAL DEVELOPMENT Opening the Platform Network “Black Box” This chapter is divided into three parts. First, I further motivate the need to develop an approach for analyzing platforms’ network dynamics. Second, I advance an analytical framework by extending network theory. Third, I use the framework to develop a set of hypotheses. To begin, I synthesize points introduced in Chapter 2 to highlight three interrelated tensions and corresponding paradigmatic pivots directing the development of an analytical approach focusing explicitly on platforms’ actual network organization. The three items highlight and address paradigmatic concerns around theoretical assumptions, level of analysis, and unit of observation. First and foremost, the network dynamic approach relaxes contentious paradigmatic assumptions by accepting heterogeneity in three key areas: (1) platforms themselves, (2) platform components and, as a result, (3) the emergent organization of platform activity. The bulk of extant platforms research suggest that network effects can be inferred through network size (e.g., see Afuah, 2013). When platforms and components are homogenous, network dynamics can perhaps be reduced to a singular mechanism (i.e., network effects) ascertainable through a singular metric (i.e., network size). However, scholarship increasingly rejects the validity of these assumptions (i.e., homogeneous platforms, components, and activity organization). Taken together, research increasingly suggests that platform network dynamics—which are critically important—cannot be validly inferred through network size alone (e.g., Cennamo & Santalo, 2013; Song et al., 2018). The complexity of platform networks should not be overlooked or assumed away in a black box. Yet, a coherent and cohesive network organization-oriented research paradigm remains notably absent from platforms scholarship. 50 Second, the proposed theoretical perspective focuses analysis at the network level. A central axiom underpinning platforms research is that pertinent platform outcomes (e.g., survival, growth, decline, etc.) are determined at the network level (e.g., Evans & Schmalensee, 2010; Iansiti & Levien, 2004; Rochet & Tirole, 2003; Srinivasan et al., 2004). While ample research elaborates the myriad strategic levers (e.g., Boudreau, 2010; Weyl, 2010) and maneuvers (e.g., Rietveld et al., 2019; Zhu & Liu, 2018) available to platform administrators (or, “sponsors”), the corresponding mechanisms—which manifest at the network level—remain obscured. Extant research does not actually know how these strategic levers impact platform networks. The importance of analyzing platform dynamics at the network level is motivated by the fact that firms’ strategic upstream levers mechanize downstream effects at the network level: without analyzing the network, platform strategy—including considerations of how platform managers direct resources and orchestrate their networks (e.g., Rietveld et al., 2019; Zhu & Liu, 2018)—cannot be fully understood. Elaborating on the complex organization ensuing from platform configurations requires network level theory. Third, component activity should provide the theoretical and empirical building block (i.e., unit of observation) for a network organizational research paradigm. A theoretical and empirical fissure exists when network effects, which incorporate the complementary benefits from platform networks’ component scale and scope, can no longer be inferred from network size alone. I posit that the implications of network scale and scope lie in their translation to platform activity (i.e., activity made possible by the platform)17. Moreover, activity provides a means to theorize and observe platforms’ de facto organization as opposed to its hypothetical 17 Activity in the broad sense—watching a video on YouTube is direct YouTube platform activity, however it also produces indirect activity (e.g., calling code) for the various technological platforms underlying YouTube’s technological stack (e.g., Python, Apache, MySQL, etc.). I elaborate opportunities for further theoretical development that are enabled by a multi-layer (i.e., vertical) view of platform activity in Chapter 6: Discussion. 51 structure. The problem of analyzing platforms’ network organization, and its implications, cannot be resolved through network size-based inference. Understanding platform networks’ emergent organization through manifest behaviour (i.e., activity) is centrally important to progressing platforms scholarship when actual behavioural dynamics are called into question. Under a behavioural perspective, platform actors are no more omniscient, homogeneous, nor rational than actors in a firm centric world (see, e.g., Cyert & March, 1963). Instead, noting shifting environments, organizational inefficiencies, and suboptimal configurations as a reality of platform dynamics builds a foundation for understanding actual platform mediated behaviour. For instance, network scale and scope can generate more noise (e.g., search costs) than value as a result of ineffective organization (e.g., Brynjolfsson et al., 2011). Indeed, research supports a nuanced view of platform network externalities, suggesting that it is often not platforms’ network quantities but rather network qualities that determine platforms’ competitive outcomes (Cennamo & Santalo, 2013; Shankar & Bayus, 2003; Zhu & Iansiti, 2012). Platform activity acts as the building block of network organization; and is perhaps the only avenue for connecting how upstream levers (i.e., platform policies and protocols) and top-down design couple with emergent bottom-up organization and actor behaviour. In capturing actual behaviour, platform activity also provides a functional performance outcome for platform analysis. Shifting towards a network dynamic view of the platform implies paradigmatic differences between extant perspectives and this dissertation’s proposed approach to platform analysis. The core distinctions between this dissertation’s approach and extant perspectives are a shift from stable environments with closed and perfect platform networks to dynamic environments with open and imperfect platform networks. For instance, relaxing assumptions around boundaries provides an agnostic approach which can accommodate analyses capable of 52 handling platforms with any degree of boundary rigidity and openness. In contrast, assumptions around network connectedness are constrained; with networks conservatively—realistically—assumed to be sparsely connected rather than fully connected. Table 3-1 below outlines the juxtapositions between this dissertation’s approach and extant perspectives (i.e., primarily from industrial economics and technology management): Table 3-1: Summary of Extant Platform Perspectives versus Proposed Perspective Extant Perspectives Proposed Perspective Environmental Regime Stable Dynamic Level of Analysis Network/Platform Network Unit of Analysis Network Side/Platform Activity Network Defining Basis Membership/Dependence Activity/Participation Locus of Network Development Membership size Activity organization Network Boundaries Rigid and High Open and Low Component Locality Fixed and Internalized Transitive and External Network Connectedness Completely Connected Sparsely Connected Adopting a Network Ecology Approach to Platform Analysis This dissertation’s network dynamic approach draws upon the network ecology and network science paradigm (Barabási, 2016)18. Network ecology originated from bioecology to 18 I adopt the “network ecology” terminology over the more general “network theory” label for several reasons. First, network ecology places a more specific emphasis on interactions instead of the more abstract tie/link/edge connection label employed in graph theory. Second, the ecology lexicon already has a clear presence in the platforms discourse; with platform environments often construed as ecosystems with central keystone actors, for 53 study interaction structures, such as food webs, within ecosystems and is an analytical approach for formalizing interaction structures (i.e., links) among entities (i.e., nodes). This approach has found theoretical applications and consistencies across a wide range of contexts (e.g., from pollinators and plants in natural ecosystems to designers and contractors in the New York garment industry; Saavedra et al., 2009; Saavedra et al., 2011). Network ecology is primarily used in biology to study natural ecosystem dynamics (Olesen et al., 2008), stability (Montoya et al., 2006; Thébault & Fontaine, 2010), and evolution (Proulx et al., 2005) through interaction networks. Similar to how natural ecosystems shape interspecies interaction, platforms are viewed as systematizing interactions among multiple groups (or, “sides”) of actors. The types of interaction are contextual to the platform, with core interactions comprising the primary units of platform value (Parker et al., 2016). As structures consisting of distinct interactions (i.e., links) among components (i.e., nodes), platform networks fit the network typology template. The parallels between interactions within natural—as well as social (e.g., Saavedra et al., 2011)—ecosystems and interactions among platform components suggest that there is merit to extending concepts originating from network ecology to studying platform activity. Although a network approach may be suitable for studying platforms’ activity dynamics, it is worthwhile to note that network ecology differs from the more well established network-based approaches in the organization studies literature. While established network perspectives examine entities (i.e., social actors) in their environment (e.g., see Borgatti & Foster, 2003; Salancik, 1995), a network ecology perspective examines the environment (i.e., network) as the level of analysis. Network oriented organizational research has example. Third, I believe the theoretical extensions from ecology for understanding platform dynamics expands beyond network ecology—a point I discuss further in Chapter 6: Discussion and Conclusion. 54 also predominantly focused more on stable relational ties and ego-centric networks over dynamic interactions and structural organization; which are emphasized in network ecology. Network ecology offers resolution to the three paradigmatic concerns introduced earlier in this chapter: incorporating emergent heterogeneity, asserting network level analysis, and building on activity as the unit of analysis. First and foremost, network ecology provides an explicit approach to conceptualizing and analyzing network organization. The ways in which network components (i.e., nodes) and the network itself vary are denoted topologically. Network topologies are graphically represented using nodes (typically as circles) and relational ties (typically as connecting lines). Platforms’ underlying networks can be depicted similarly, with components represented as nodes and interaction activity represented as directed ties. Denoting network organization in terms of platforms’ composite activity structure places the platform network at the theoretical and empirical fore. Platforms’ underlying network structure can vary substantively (Afuah, 2013), even given identical levels of activity and network size. Network ecology provides a well-developed lexis for rendering network structure and its variation. Network Activity Framework This dissertation’s approach relies on two elements: component activity and—subsequently—components themselves. Both elements are contextual to the platform. Components. A component is any entity systematized by the platform. Components generally take the form of a complement (i.e., good or service representation) or complementor (complement producer). I also categorize actors (e.g., individuals or organizations that instantiate platform activity) as components. By abstracting any entity mediated by the platform as a component, the theoretical framework makes no inherent assumptions around component 55 properties or categorizations. Rather, these aspects become apparent through their position in the network’s activity structure. Activity. A single instance of activity refers to an action that is mediated (i.e., made possible) by the platform (i.e., platform use). I categorize activity into two forms: interactions (component to component activity) and innovations (the addition of a new component, or component dependency, to the platform). This model framework aims to be flexible and generalizable to entities that can be defined as a platform—any structure that systematizes (i.e., enables, mediates, and constrains) components or their connections by means of authentication (i.e., validating the component or connection). More specifically, activity refers to ex-post enacted (i.e., realized) connections. Connections can be viewed as horizontal (i.e., component to component interactions) or vertical (i.e., component to platform innovations). Empirically, both connections are contextualized by the platform. For example, interactions can take the form of a payment on a credit card network, booking on a travel platform, or sending a message on a messaging platform; while innovation activity can take the form of posting new content on a media platform, releasing an app onto a marketplace, or simply registering on a platform. This framework is activity centric in that it utilizes network activity in two primary ways: Activity as performance. First, it frames network activity as platforms’ key performance indicator. Activity provides a direct standard for network performance; and overcomes network size’s validity concerns, particularly in low adoption barrier contexts (which characterize many contemporary digital marketplaces). Contemporary digital platforms aptly use “monthly active users” (MAU) as a key performance indicator to better provide details on a platform’s active network size19. What better platform performance measure is there, beyond its actual use? 19 Note that activity volumes, though useful as a theoretically abstracted performance indicator, does not completely capture the potentially heterogeneous value or quality of activity. However, I do argue that the quality of activity is 56 Activity organization. Second, activity provides useful information about the ways in which platform networks are organized. Specifically, activity can be used to build out network topologies. A general platform model facilitates two forms of activity: component innovation and component interaction. Innovation activity is analogous to a component joining the platform network. Interaction activity occurs when one component interacts with at least one other component through the platform. Both forms of activity represent a platform’s functional performance, and are interdependent (though not necessarily mutually). Innovation activity generates additional opportunities for interaction, while interaction represents the actualization of a platform’s value proposition. Therefore, representing platforms’ network activity organization requires only two elements: components, and the interactions that connect them. Components are heterogeneous both intrinsically (Saadatmand et al., forthcoming) and in the ways they are organized within networks (Venkatraman & Lee, 2004). Therefore, a component’s impact becomes apparent through its interactions (i.e., horizontal connections) with other components (e.g., Afuah, 2013). This approach follows the dissertation’s overall view that networks’ emergent organization should be formally incorporated, rather than presumed. An ex-post activity approach reverses the path of theoretical inference, relative to extant network size-based approaches. Centering analysis on realized network activity infers that platforms’ internal and external contingencies coalesce and unfold in such a way that activity organizes as observed. In other words, this approach assumes that platform level settings (e.g., captured in the way in which activity is organized. As an extreme example, suppose a messaging platform is invaded by spambots. These spambots would add to the platform network’s size. However, the lack of quality would fail to promote meaningful topological connections throughout the platform network; leading to subsequent declines in activity. 57 policy, design, etc.) in conjunction with external environmental factors generate the conditions for the emergent activity topology for a given timeframe. Rather than assume network effects from network size, the present approach diagnoses upstream dynamics through network activity. By focusing on network activity dynamics, the framework explicitly attends to the network topological mechanisms that form from—and ought to guide—platform configurations. Framework initialization. The basic platform network activity framework requires four parameters to be clearly defined: (1) the platform itself, (2) the representative interaction(s), (3) the component(s), and (4) a meaningful configuration of time spells for empirical analysis of sufficiently detailed network moments. First, an appropriate context should be established because most structures can fit the broad platform definition. A platform is defined as an entity that systematizes components through authentication. It is up to the analyst to identify worthwhile phenomena to conceptualize as a platform. Second, the analyst must identify an appropriate interaction, or set of interactions, through which to construct the network activity structure. Under this theoretical framework, a platform mediates a singular form of valued interaction among components. I argue that so long as the analyst selects a representative interaction (e.g., viewing for media platforms, purchasing for marketplaces, etc.) the general network activity topology remains intact for analytical purposes. Moreover, platforms are typically associated with a readily identifiable “core” interaction. The present approach assumes that all secondary interaction types are incorporated in supporting the primary “core” interaction; and that their effectiveness will manifest through this core interaction20. 58 Third, the component unit(s) must also be appropriately defined. A platform component is broadly defined as any entity (e.g., object, individual user, organization, etc.) that depends on the platform for interaction. A product-based platform market typically consists of users and complementors. Complementors introduce complements (i.e., products, as innovation) onto the platform market that users can engage with (i.e., consume, as interaction). Complementors can be consumers as well producers21. The framework allows for component encapsulation and varying degrees of granularity in defining components’ unit of analysis. For example, a component can be defined in terms of users and complements; these complements can be further encapsulated into their higher level complementors. While more granular component declarations (e.g., complements instead of complementors) may yield greater detail, networks’ overall organization will be captured regardless of the level granularity. In general, the level of platforms’ component cross-functionality dictates the limits of component granularity. Given an interaction-focused framework, where network connections represent interactions, component innovations are not directly incorporated22. When more producers are also consumers (i.e., higher cross-functionality), defining such components as complement (i.e., product) instead of complementor (i.e., producer) inherently eliminates interactions produced by the complementor because complements are interacted with and typically do not initiate interactions. In high cross-functionality contexts, opting for complements over complementors washes out the more important interactions generated by complementors (i.e., producers) in their capacity as 21 This point is overlooked in the extant platforms literature. Including the flexibility for a complementor to also be a user can be important, particularly given a more detailed network topological approach. This key theoretical advance is introduced in this dissertation as cross-functionality. 22 Although it is possible to expand the framework to incorporate innovations more explicitly, this dissertation opts for parsimony over the complexities associated with theorizing an innovation layer to overlay the present model framework. I explore future directions with respect to the addition of component innovation in Chapter 6: Discussion and Conclusion. 59 interaction initiators (i.e., consumers). When there is clear separation between users (i.e., consumers) and complementors (i.e., producers)—or negligible consumption from complementors—then complementors can be further decomposed in terms of their complements (i.e., products) without substantively compromising the higher resolution topography. Therefore, a conservative approach is to default components in terms of the highest-level unit (i.e., typically users and complementors, rather than users and complements). From there, the platform context informs the potential alternatives and level of granularity for component definition23. Fourth and finally, an appropriate timeframe and corresponding observation cutpoints must be considered. These cutpoints partition the timeframe into observation windows, or time spells. Because the framework aims to tap into platforms’ realized activity, lengthening temporal windows inherently trades off observation count for detail. Network detail improves asymptotically with increasing observation time. The longer the temporal window for observation, the more detail—but at a diminishing rate. While networks likely won’t suffer from detail saturation, undersampling due to a prohibitively short time window can fail to construct a faithful network representation that adequately incorporates the mix of its internal and external dynamics. The challenge is further exacerbated when observing a platform network with large interaction variance, or when attempting to conduct testing (e.g., to capture policy implementation impact). Therefore, the analyst must declare a temporal observation window that balances detail with observation count and its accompanying statistical implications. Taken together, these minimum requirements set up the general framework for analyzing platform activity dynamics. Table 3-2, below, provides a few examples of platform contexts in terms of their representative interactions and components. 23 I discuss this matter in greater detail in Chapter 6: Discussion and Conclusion, including the approach and implications for constructing complement(or) and/or consumer centric weighted graphs. 60 Table 3-2: Platform, Interaction, and Component Examples Platform Context Interaction Example Component Example Content (e.g., Digital video, audio broadcasting) Consuming content Consumers and publishers/content Marketplace (e.g., eBay, App store) Completing a transaction Customers and vendors/ products Payment (e.g., VISA, PayPal) Completing a payment Users (senders and receivers) Digital Video (e.g., Netflix, YouTube) Watching a video Viewers and publishers/videos Audio broadcasting (e.g., Spotify, Radio stations) Listening to a song Listeners and artists Operating systems (e.g., Windows, Linux) Using an application Users and publishers/applications Spoken languages (e.g., English, French) Speaking Speakers and listeners Network Topology and Mechanisms Topology. I proceed by introducing network topological properties; and formulate hypotheses accordingly. Specifically, I characterize networks in terms of connectance, centralization, clustering and centralized clustering; then finally elaborate on network motifs as a means of representing a network’s degree of cross-functionality. This “5C” framework provides an accessible and comprehensive way to characterize platform network organization. To introduce some topological properties, I refer to Figure 3-1: 61 Figure 3-1: Network Topology Example Connectance measures the degree to which a network is connected. The more connections (i.e., lines linking components), the higher the connectance. Centralization measures the degree to which a network is concentrated. The components on the network perimeter have fewer connections than the components approaching the network’s centre. Figure 3-1 differentiates the high centrality components (in blue) from other components. Network level centralization captures the disparity in connections among components. Clustering measures the degree to which a network exhibits dense groupings. There are complete clusters among the four components at the network centre that contribute to network level clustering, but one among three other components at the bottom of Figure 3-1. Centralized clustering measures the degree to which a network exhibits dense groupings among high centrality components. The same four components in the network centre are high centrality and thus eligible—and they contribute to the network’s centralized clustering due to their clustering. By contrast, the cluster at the bottom is not considered due to the constituent components’ insufficient centrality. Cross-functionality 62 measures the degree to which a network exhibits functional diversity among its components. This particular property makes use of adjacent directional motifs and will be explained in greater detail at the end of this chapter. Essentially, however, cross-functionality leverages network motifs to detect the prevalence of sequential motifs specifically (i.e., in purple). This particular motif indicates components’ degree of network multi-siding (i.e., interacting in multiple capacities). These properties reflect various distinct structural facets. Taken together, they provide an initial vocabulary to describe platform network organization. I elaborate in depth on each of these properties and how they relate to network activity in the hypotheses section. Incorporating cross-functionality in particular is a key theoretical advance in that it addresses the multiple hats nature of actors; an important yet largely disregarded platform aspect (an exception is Afuah, 2013, pp. 263-264). By leveraging directional motifs, I develop a formal approach to measure the degree of cross-functionality in a platform network. Mechanisms. These topological properties relate to networks’ efficiency and resilience; general mechanisms shaping system dynamics. Whereas these mechanisms typically characterize network systems in a more or less stable equilibrium state, a topological view is appropriate for diagnosing the interaction structures that organize as a result of these mechanisms in conjunction with their dynamic internal and external environments. This dissertation’s analytical framework does not suppose that a system is universally efficient or resilient—rather, efficiency and resiliency manifest heterogeneously within a network, and are subject to dynamic contingencies. Network topology provides a footprint to extrapolate networks’ mechanism-enacted organization while maintaining flexibility around internal and external dynamics. 63 The mechanisms can coincide in complex ways. While efficiency focuses on the internal organization of network flows, resilience emphasizes structural robustness with respect to (predominantly) exogenous disturbances. In some cases, these mechanisms are diametrically opposed. In other cases, they are independent of each other; or occur in tandem (Bascompte et al., 2003; Bastolla et al., 2009; Shi & Mondragon, 2004). A classic approach for illustrating the network topological variance in resilience and efficiency is to contrast archetypes. Resilience and efficiency can be explained simply by contrasting a regular ring network with a fully centralized star network; as in Figure 3-2, below. Figure 3-2: Centralized Star and Regular Ring Networks Efficiency relates to a network’s capacity to transmit from one node to another, and is often evaluated in terms of path length (i.e., connective steps between nodes). In Figure 3-2, the star network exemplifies an efficient configuration while the ring network represents an inefficient configuration (given the number of nodes and connections). In the former, a single node bridges any given node to each other node; providing a direct path by acting as a hub. In the latter, nodes are sequentially connected; reaching the furthest point from any given node requires 64 passing through multiple successive nodes. In a market context, a more efficient network is akin to a “denser” configuration. That is, an efficient network provides greater accessibility because fewer junctions are required to reach one point from another. Resilience describes a system’s capacity to “absorb disturbance24 and reorganize while undergoing change so as to still retain essentially the same function, structure, identity, and feedbacks” (Walker et al., 2004). From a network topological perspective, a disturbance is typically depicted as the loss of nodes, connections, or both. In the star network, a single point of failure exists. Once the central hub is removed, all connections are lost; along with the network structure altogether. In contrast, removing any single node in the ring network has a less disruptive overall effect in terms of altering the network’s structural integrity. Highly centralized networks are thus typically viewed as being more fragile yet more efficient (Albert et al., 2000). Dynamic Network Topology Approaching network analysis dynamically presents challenges in directly incorporating theoretical mechanisms because resilience and efficiency are typically considered stable and global network properties. Moreover, maintaining theoretical flexibility around heterogeneity in platform networks’ internal dynamics (e.g., scaling boundaries, policy shifts, etc.) and external contingencies (e.g., competitive environment, institutional shifts, etc.) in conjunction with the potential for localized network profiles introduces analytical complexity. In contrast to classic network resilience models, the present approach does not presume that node and link changes follow a random or targeted regime. Rather, network configurations emerge through platforms’ 24 A wide variety of terminology across scientific fields is used synonymously with disturbances; including shocks, jolts, perturbations, and shifts. 65 coalescing internal and external dynamics—both of which can manifest in heterogeneous ways, at a given temporal period. To accommodate for the added theoretical flexibility, this dissertation takes a network inferential approach towards these theoretical mechanisms. A network is resilient to the extent that it maintains its structural integrity, and efficient to the extent that it condenses its nodes. Resilience and efficiency are ultimately expressed in how a network is integrated. Integration refers to the degree to which a network is interconnected—or, in some cases, present at all. Any network, which is constructed with n nodes and v links, features a maximum v that changes exponentially25 with n. Positive feedback between platforms’ underlying network size and value explain the potentially explosive scaling properties inherent to contemporary digital platforms (Choudary, 2015). Perhaps the most popular explanation and representation of this relationship is Metcalfe’s law, which models network value as proportional to the number of possible links, v, between nodes, n: 𝑣 = ௡(௡ିଵ)ଶ, which is parsimoniously approximated as v ∝ 𝑛ଶ ; (3.1) where all nodes can connect to each other Due to the exponential relationship between network connectivity and size, the number of unique network configurations also increases exponentially as the number of actual links falls further from its maximum, v (and approaches the midpoint, v/2). This structural characteristic is particularly remarkable because real world networks are actually sparse, and far from complete 25 Using the term “exponentially” is technically incorrect. Network scaling dynamics technically follow a polynomial—specifically, quadratic (i.e., to the power of 2)—trajectory. However, the “exponential” terminology is widespread in the network effects discourse. I continue to follow this convention throughout the dissertation with the caveat that, while it captures the essence of an increasingly rapid trend, it is not technically correct. 66 (Barabási, 2016)26. A large and sparse network can be configured in a multitude of ways depending on the number of links and nodes; and a large portion of configurations do not represent interconnected networks. For example, a network with one connection for every two nodes can form an array of distinct dyads (node pairs), but lack the structure required to form an integrated network. Conversely, a network with fewer, but more densely interconnected, links can configure a highly integrated network structure (e.g., a star network). Just as the present approach rejects the potential for fully connected platform networks, it also cannot assume that networks’ composite nodes and links necessarily organize into an efficiently integrated structure. Network integration incorporates, yet is distinct from, efficiency. While efficiency focuses on geodesic flow (i.e., path minimization) between nodes, integration pertains to the connective density of the network structure as a whole. Although highly integrated networks are likely more efficient overall, efficient networks are not necessarily more integrated. The two properties overlap to the extent that networks are dense (e.g., as in the star network), which generally increases efficiency as well as overall accessibility (i.e., more reachable nodes). However, localized efficiencies do not necessarily aggregate into a globally accessible network. For example, assume that the two networks in Figure 3-2 are organized by a single platform. In other words, the platform organizes two distinct and unconnected communities. Whereas adding a new connection within either of the two networks improves overall efficiency (particularly for the ring network) without improving network access, adding a connection across the two 26 This further highlights an interesting disconnect. Combinatorics places the maximum unique network arrangements at v/2. Whereas theoretical models assume fully connected networks, the fact that real world networks are actually sparse (i.e., less than v/2 connections) inverses the combinatorial implications of adding or removing connections from a network. That is, subtracting links increases the possible network configurations for networks with more than v/2 connections, yet decreases the possible configurations for networks with less than v/2 connections. This point is not of particular importance to this dissertation, but illustrates that erroneous initial assumptions can risk detriment to ensuing theory development. In contrast, a theoretical framework resting on random network configurations would likely be more substantively impacted by overlooking such characteristics. 67 networks improves integration by expanding overall network scale. Figure 3-3 demonstrates how sparsely connected networks can vary in efficiency and scale. Figure 3-3: Integrative Variability in Network Efficiency and Scale Efficiency Scale Incorporating integration is important to a network dynamic approach for three key reasons. First, real world networks are sparse (e.g., Barabási, 2016). Elaborating on integration is particularly because it relaxes the assumption of complete network connectivity. In doing so, this dissertation’s approach does not presume that a platform network consistently operates as an integrated whole. A platform network can be composed of multiple efficiently linked subnetworks that are not interconnected, just as it can be characterized as a singular integrated 68 network with low density (i.e., efficiency). Networks’ integration is particularly important in the context of large sparse networks given that networks can theoretically organize in an exponentially increasing variety of ways according to the number of nodes while also facing contextual constraints (e.g., spatial, temporal, etc.). For instance, platform networks can splinter into several smaller subnetworks (of varying size) as opposed to maintaining a singular integrated structure (e.g., geographically localized platforms such as ridesharing, meetup, and neighbourhood platforms). Due to networks’ nonlinear connective scaling dynamics, a platform with n nodes divided into discrete subnetworks, s, realizes substantively diminished network effects compared to an integrated n node platform network. These differences become more pronounced with increases in n or s. Therefore, network integration can not be taken for granted when increasingly broad varieties of network organization are possible. Second, real world networks are dynamic. Large persistent networks have been found to organize in an accessible and efficient scale-free configuration (Barabási & Albert, 1999) resembling the top-right tree graph in Figure 3-3. The scale-free feature suggests fractal scaling—i.e., that the overall configuration would be retained regardless of network size. The theoretical mechanism driving scale-free growth, known as preferential attachment, posits that networks grow as new nodes attach to pre-existing nodes in proportion to their centrality (Barabási & Albert, 1999). While the theory behind this network scaling mechanism concerns within-network growth, the data used to induce it is notably cross-sectional; and exemplary in its survivorship bias. Indeed, studies continue to uncover imperfections in the theory’s position on network scaling dynamics. For example, in Broido and Clauset’s (2019) study of over 900 real world networks finds that most networks fall short of forming the power law distribution suggested by the scale-free network axiom. Similarly, studies such as D'Souza, Borgs, Chayes, 69 Berger and Kleinberg (2007) find that preferential attachment, in actuality, is likely tempered by structural constraints; while others suggest that it is not solely popularity, but also similarity, that drive network attachment dynamics (Papadopoulos et al., 2012). In sum, nuanced, multifaceted, and numerous mechanisms explain network dynamics. Centering analysis on network integration provides a flexible approach that can accommodate these complexities. Third, network integration is conceptualized and operationalized topologically. Topological representations provide a direct interface to adapt network theory; and formally denote resilience and efficiency. Network theory provisions a rich inventory of topological concepts to characterize network integration. Analytical Approach Echoing dynamic network topology studies in fields including neuroscience (Bassett & Sporns, 2017) and biology (Middendorf et al., 2005), and dynamical inference approaches more broadly (Katz et al., 2011; Vicsek & Zafeiris, 2012), this dissertation extrapolates systems’ structural qualities via the topological signatures generated through platform activity. As platform networks’ internal and external dynamics coalesce in a temporal period, the resulting activity formation indicates the networks’ underlying integration. In other words, network activity is the direct enactment of a platform’s capacity to organize under a given environmental regime. When platform policies are misaligned with the environment, diminished efficiency and resilience will be reflected in the integration of network activity—rather, its disintegration. In turn, the scaling trajectory of subsequent network activity will taper commensurate to the degree to which network integration is compromised. When the platform is misaligned with its 70 environment, the functional deficiencies will deter future network activity. Conversely, the better integrated the network, the greater the expected activity. An alternative way of construing the analytical approach is as a feedback loop between the integration and subsequent “stocks” of network activity. Suppose a stock of network activity is allocated to a platform during a time period. Subsequent activity stocks scale depending on the configuration of network activity (i.e., representing platforms’ integrative capacity). When platform networks are able to maintain a stable integrative configuration as they scale, then the ensuing allocation of activity stocks will maintain a stable growth trajectory. However, as the topology of activity increasingly (dis)integrates, subsequent activity stocks can be expected to (de)escalate due to the platform’s environmental (mis)alignment. Figure 3-4 below illustrates the relational dynamics between network integration and activity. Figure 3-4: Relational Dynamics between Network Integration and Activity 71 Suppose that curve 𝑀ഥ represents an activity-sustaining integration frontier. That is, for a given level of network activity, there is a commensurate integration profile which maintains the activity level into future time periods. Given a time-dependent activity level, α(t), integration can exceed (e.g., ṁ) or fall short of (e.g., ṃ) an activity-sustaining configuration. The implications for subsequent time periods, e.g., t+1, are that activity stocks adjust according to the deviation from the activity-sustaining integration configuration. When actual network integration exceeds the activity-sustaining profile, as in ṁ, the theory suggests that following activity stocks will grow. Conversely, in the case of ṃ, proceeding activity stocks are expected to shrink due to the diminished integration. Put plainly, is this dissertation’s very thesis: the better integrated a platform network’s current activity, the greater its future activity quantities. The following hypotheses revolve around characterizing a network structural dimension and elaborating its impact on activity growth—or, conversely, decline. Before continuing, it is important to clarify the "activity growth" terminology. The term "growth" suggests positive increase. However, this dissertation places growth and decline on opposite ends of the same continuum. Therefore, negative growth (i.e., decline) is just as present—and of as much interest—as positive growth. The decision to use "growth" is to align the terminology with the latent growth curve modeling approach used to analyze this dissertation's data. The approach is introduced in Chapter 4: Methods. Throughout the remainder of the chapter, I formulate the relationship between network structural properties and activity growth in terms of two network mechanisms: resilience and efficiency. Networks organize in ways that reflect their resilience and efficiency. Though the latter mechanism’s relationship on activity growth is fairly obvious—more efficient networks promote activity growth—the former may not be as clear with respect to activity growth. It is for 72 this reason that the “growth” terminology must be taken as a continuum which includes a negative range. Therefore, while the relationship between resilience and activity growth is less clear, the relationship between resilience and activity decline is more intuitive. That is, network resilience buffers activity decline. While topological concepts continue to garner development within the broader network sciences, I take an introductory approach to outlining their general implications within a platform network context. More specifically, I highlight how connectance, centralization, clustering, centralized clustering, and cross-functionality characterize network integration and, through it, provide insight into the evolutionary trajectory of network activity; and platform dynamics more broadly. Though far from incorporating the cutting edge of network science, this approach fits this dissertation's goal of synthesizing an accessible network dynamic view for platform analysis. Connectance Connectance27 is a fundamental network property referring to “the fraction of all possible links that are realized in a network” (Dunne et al., 2002). In essence, connectance represents the extent to which a network actually exists28. Where connectance is the realized set of connections in a network, a network’s potential set of connections is known as its connectivity. The latter determines the former, and is a function of network size. Appraising a platform’s value in terms of its underlying network size, or “installed base,” is widespread convention (e.g., Eisenmann et al., 2006; Zhu & Iansiti, 2012). Inferring network value from network size holds advantages such as parsimony, ease of measurement, and discursive accessibility. However, the fundamental 27 Also referred to as density. 28 Connectance differs from integration in that the former emphasizes structural quantities; not qualities. 73 rationale of network effects is that size approximates connectivity—which is in turn realized as connectance—and that network effects scale to the extent that platform actors can (i.e., connectivity) but ultimately do connect (i.e., connectance). Without axiomatic assumptions of complete network connectance (Afuah, 2013), inferring value from network size is no longer a viable theoretical approach. Therefore, examining platforms’ underlying network connectance is essential to interpreting realized network effects. Most platform networks never realize their fundamental connectivity (i.e., all actors interacting with all other possible actors). In fact, most real networks are only sparsely connected (Barabási, 2016). Platform level aspects including curation improvements (e.g., machine learning based recommender algorithms) generally improve the connectance prospects of contemporary platforms (Becatti et al., 2018). However, some connectivity frictions and disparities are fundamentally greater than others. For example, platforms that coordinate activity involving geographically constrained components (e.g., ride hailing, accommodations, etc.) face limits that completely digital interactions do not. In such cases, only a fraction of a platform’s total network of components is technically available to any given actor and connectivity is significantly lowered at any given network size. Connectance is a dynamic property that can change as platform networks evolve. Platform policies that optimize network connectivity for a particular size range may be poorly suited for larger or smaller size regimes. Given that components and preferences are heterogeneous, even fewer components are actually relevant to any other given component. Actors (which interact with platform components) rarely need, or desire, to interact with all other available components. Moreover, connectance will naturally decrease with size if components (e.g., participants) are constrained in the amount of activity they can generate (e.g., due to time constraints) and because linear changes in network size equate to theoretically 74 exponential changes in connectivity29. Interaction dynamics can emerge based on actor-driven selection (e.g., bottom-up) as well as platform-driven matching (e.g., top-down). Figure 3-5 illustrates the difference between high and relatively low network connectance, supposing identical size and activity levels. Figure 3-5: High versus Low Network Connectance High Connectance Low Connectance Connectance represents the degree to which activity is distributed across the network. Network activity can be distributed horizontally (based on interactions) as well as vertically (based on innovations). Therefore, holding constant network size and activity, connectance depicts the ratio of interaction activity to innovation activity. These two forms of activity represent different stages of platform functionality. While innovations generate opportunities for interaction, interactions represent realized platform activity. Diagnostically, connectance provides evidence that the platform’s momentary configuration subject to its external environment organizes a greater proportion of actualized interaction activity relative to untapped innovation activity. In contrast, lower connectance can indicate a greater stock of components 29 This point is elaborated in Chapter 2: Literature Review. Empirical techniques (i.e., transformations) are available to accommodate for these scale-driven dynamics. I elaborate further on these techniques in Chapter 4: Method. 75 that have yet to realize interactions. A greater momentary proportion of idle components can be suggestive of top-down inefficiencies such as ineffective market curation as well as bottom-up impediments such as prohibitive noise in the network or component discovery process. Tapping connectance as diagnostic of interaction-to-innovation activity is particularly important in light of growing research which suggests innovation activity in and of itself does not necessarily stimulate network effects (e.g., Afuah, 2013; Boudreau & Jeppesen, 2015). Another interpretation of lower connectance, given fixed network size and interaction activity levels, is as the concentration of repeat interactions among components (i.e., connectance as interaction distribution). For example, take an extreme case where each component interacts repeatedly with only a single component (e.g., due to the absence of a network discovery or feasible curation mechanism). Compared to a platform mediating access to a variety of components, greater experiential salience may be attributed to the component as opposed to the platform it is accessed through (e.g., Kelley & Michela, 1980). In such a case, platform value (i.e., appeal) is contingent entirely on providing access to the singular component as opposed to multiple components representing the network as a broader entity. Should interaction with the single component become possible through substitute means (e.g., via competing platforms), or if the component is no longer available, the platform’s appeal to the participant is diminished substantively—if not entirely. These micro-level dynamics around platform versus component appeal aggregate upward to the network level. Lowered connectance signifies that activity is increasingly constrained between select components as opposed to being dispersed throughout the network (i.e., market or community). Connectance can also attenuate the appeal of competing platforms by framing alternative seeking as less attractive. Particularly if the broader market—which can be organized and 76 accessed via multiple platforms—is crowded, greater market density (i.e., connectance) provided by a single platform may provide resilience against the departure of activity for substitute platforms. This consideration is especially important in contemporary digital platform contexts; where access is significantly more open and fluid compared to 20th century network markets (e.g., Cusumano et al., 1992; David, 1985). Denser network structures can represent platforms that are facilitative of broader market access and coordination. When actors are able to sufficiently satisfy their market demands via a single platform, the marginal benefits of adopting and maintaining membership on additional platforms are lower relative to their perceived marginal costs. Commensurate to Herbert Simon’s (1955, 1956, 1957) foundational theory of search and satisficing, individuals are limited in their cognitive capacity to manage information and are apt to disengage from search after achieving satisfactory utility (e.g., Caplin et al., 2011). In receiving adequate market access and coordination through a focal platform, actors are less likely to engage in costly search and trialing of platform alternatives within the same space. As a result, connectivity—as reflected through connectance—can act as a competitive deterrent against the migration of activity onto substitute platform(s). The proportion of actors with insufficient market response are more likely to search the broader space (i.e., other platforms). In aggregate, platforms providing more network-attributable (versus component-attributable) appeal develop a more robust value proposition and consequent capacity to promote platform—as opposed to component-specific—activity. This argument draws from the natural ecosystems literature, which suggests that greater network density grants the broader system superior resilience via diversity effects (Polis & Strong, 1996). That is, when each component has a broader set of available alternatives to interact with, the system develops robustness to disturbance (e.g., a substantive removal of components) as a result of this flexibility. More recent 77 research from the broader complex networks literature further corroborates the resilience of denser networks against component and link loss as a general network feature (Gao et al., 2016). Denser networks’ resilience extends beyond disturbances’ first order impacts as system failures typically unfold in a cascading fashion. That is, an initial network compromise begets further network decay—generally according to dependence-based dynamics (cf. Uzzi, 1997). As connectance indicates substitutability at the component level, denser networks benefit from a greater threshold against such second order cascades. In sum, a denser interaction structure (i.e., higher connectance) is expected to positively impact subsequent platform activity: H1: Network connectance is positively related to activity growth. Centralization Centralization refers to the structure30 of networks’ component degree distributions, and is typically visualized as a density distribution graph of the proportion of components with a given number of network ties. Examining platform networks’ centralization is analogous to understanding the distribution of interaction activity among components. Higher centralization signifies greater skew in the interaction distribution among components—that is, concentrating ties in a minority of components. A network with no centralization at all is one where actors are structurally equivalent (e.g., Sailer, 1978)—or, perfectly equal in their interaction profiles. 30 Structure is distinct from network size and connectivity. On a topological level, the latter two refer to the quantities of components and their connections, respectively. This dissertation’s key emphasis is on structure—how components are connected. Structural concepts such as centralization focus on network qualities. 78 Clarifying centralization’s relevance anchors on two foundational network typologies: the random graph (Erdős & Rényi, 1959) and the scale-free network (Barabási & Albert, 1999). Each typology models a distinct mechanism for network linkage, through a process whereby a network iteratively adds links under a predetermined probability regime. Early modeling approaches were based primarily on the former, which specifies a uniformly random linking mechanism (e.g., May, 1972). Specifically, each pair of nodes is linked with a pre-set probability; resulting in a Poisson degree distribution. Though instrumental in anchoring network theory, few real complex systems can be characterized as a randomly linked network. Around the turn of the millennia, Barabási and Albert’s (1999) landmark study highlighted that a diverse multitude of large complex systems ranging from genetic networks (e.g., proteins and genes) to information networks (e.g., the World Wide Web) and social networks (e.g., movie actor collaborations, scientific citations, etc.) across disciplines have network topologies that are scale-free; to varying extents (cf. Broido & Clauset, 2019). Two properties define the scale-free typology: preferential attachment and power-law scaling. First, preferential attachment dictates that networks expand through the addition of new nodes which link preferentially—not randomly—to nodes that are already well connected. That is, focal nodes link to prospective nodes in proportion to target nodes’ centrality in the network; generating a “rich-get-richer” regime. Second, the preferential attachment mechanism results in a power law distribution (i.e., as opposed to a Poisson distribution). This power law distribution is maintained throughout changes in the network’s scale, generating fractal substructures, due to the preferential attachment mechanism. The network typology is, hence, scale-free. The scale-free model has since come to guide contemporary research on complex network dynamics (Barabási, 2009). Figure 3-6 illustrates the topological and density distribution differences between a 79 typical scale-free network (i.e., high centralization) and a typical random graph (i.e., low centralization). Figure 3-6: Scale-free and Random Graph Topologies (top) and Associated Density Distributions31 (bottom) Scale-free (High Centralization) Random (Low Centralization) Density Distributions 31 Large scale-free network density distributions are also commonly log-log transformed. 80 However, more recent research finds actual scaling dynamics surrounding real-world complex networks to be nuanced (e.g., Broido & Clauset, 2019; Papadopoulos et al., 2012). In most cases, preferential attachment mechanics are tempered and subject to saturation effects (D'Souza et al., 2007). Scaling constraints can manifest at various levels, and for various reasons. Nodes (i.e., components) and networks approach structural limits. External shocks in conjunction with networks’ internal configurations can also redirect scaling trajectories. When structural limits are reached, additional growth may be increasingly difficult to generate through conventional means, and subjected to intensifying innovation pressures (cf. Lee, 2013). A successful configuration in one context or scaling regime may not support further activity growth in others. Moreover, while systems may converge towards a particular order, real dynamic networks are inherently never cemented into a perpetually stable equilibrium state (e.g., Dorogovtsev & Mendes, 2002). In sum, there exist a multitude of complexities impacting platform networks’ scaling dynamics and the precise concerns surrounding network growth varies between and within contexts. While centralization32 refers to increasing degree distribution inequality at the network level, centrality measures the relative importance of a given node within the network. Platforms characterized by high network centralization possess a disproportionate node activity structure. That is, a fewer number of actors account for a greater proportion of activity. Centrality captures the extent to which a node bridges other nodes throughout the network, or more simply its 32 Centralization as a process is also discussed throughout the network science literature. This dissertation focuses primarily on centralization as a network property, but inherently incorporates centralization as a process due its temporal emphasis on network dynamics. 81 volume of incident connections; or some variable combination of these aspects depending on the specific type of centrality33. Centrality signifies important nodes across various network contexts. For instance, bioecology oftentimes employs centrality to identify food webs’ keystone species (Martín González et al., 2010), which are critical to maintaining ecosystem order and resilience (Mills et al., 1993). Put another way, keystone species represent a natural ecosystem’s point of fragility; as the removal of a keystone species can often be the precursor to ecosystem collapse (e.g., Grover, 1994). In various other contexts including social (Schilling & Fang, 2014; Uzzi, 1997), cognitive (Bullmore & Sporns, 2012), and logistical (Guimera et al., 2005) networks, high centrality nodes act as important hubs and conduits that provide efficient routing to other nodes; organizing the broader system in general. Moreover, nodes occupying high centrality positions are generally ascribed status and power in social sciences research (Brass & Burkhardt, 1993; Ibarra, 1993; Rowley, 1997). Therefore, there are advantages and disadvantages associated with centralized network organization. On the one hand, low centralization networks are viewed as more robust to failure from targeted node loss (Albert et al., 2000). Connections are more evenly distributed throughout the network, such that the loss of any particular node will not destabilize a low centralization network to the same extent as the loss of a highly centralized node in the case of high network centralization. On the other hand, high centrality nodes can represent important network hubs and entry points. In a social network context, hubs can take the form of influential actors. Such actors can be a source of attraction and retention by legitimating and drawing attention to the platform through their membership and endorsement (Erdogan, 1999; Stuart et al., 1999). 33 I elaborate on forms of centrality in Chapter 4: Method. For further details, see Freeman (1978). 82 Onboarding and leveraging the reputations of influential actors can prove to be instrumental in populating a platform, and attaining critical mass. In other words, platforms attract and retain nodes through effective curation of activity involving central actors; also making them points of network vulnerability (e.g., against targeted removal). Platforms can attract components and curate connections through centralized hubs. Just as these centralized components can be a channel of initial or customary platform activity, they also broker access to larger communities or genres as contextual exemplars (e.g., Barlow et al., 2019). As market mediators, platforms create value by delivering interactions. By promoting activity with exemplary components, platforms curate relevance in interactions while potentially generating efficiencies through hub-oriented organizing as well. Such structural flow efficiencies manifest in the form of reduced network path lengths—that is, the connection-based distances from one node to any other. Scale-free networks inherently reduce path lengths, effectively “shrinking” the network and granting greater accessibility to components overall. The specific procedures through which platforms leverage hubs for efficiencies is contextual. For instance, digital media platforms incorporate interactions with hub components to advance interactions with relevant neighbouring components (e.g., via recommendation algorithms, comment/discussion features, etc.) while utilizing interaction data to update user taste profiles (e.g., Goldberg et al., 2001). Structural constraints can fundamentally limit the degree of potential network centralization; such as when platform activity is increasingly rivalrous (e.g., ride-hailing, food delivery, etc.)34. Activity centralization represents a platform organizing approach that successfully appropriates component relevance during a given moment. Activity networks are constantly 34 This stands in contrast to pure digital goods and services, which are typically not subject to the same spatial, temporal, and even linguistic limitations as in the case of physical deliverables. 83 reconstructed under a multitude of shifting contextual factors including the external environment and platforms’ own configurations (e.g., including policies, network size, value capture channels). Platforms’ emergent activity organization may be more centralized in some moments while less so in others. A greater degree of centralization suggests that the platform more effectively exploits hub-based activity structuring and their potential efficiencies. Google’s search engine is a prime example of a platform effectively appropriating a scale-free network organization to curate the World Wide Web (WWW) through their PageRank algorithm. The algorithm, which constructs a centrality-based webpage topology (Bryan & Leise, 2006), was definitive to the platform’s success in overtaking well entrenched incumbents as a result of its superior delivery of the WWW35. At the network level, greater centralization indicates that a platform’s momentary configuration and surrounding environment converge in such a way that fewer components account for a greater proportion of network activity. Although centralization is advantageous in generating network scalability and connectivity efficiencies, leveraging fewer components to organize and deliver activity also incurs potential disadvantages in the form of increased vulnerability against hub loss—centralized networks are thus characteristically “robust-yet-fragile” (Doyle et al., 2005). Moreover, more recent research finds that most real complex networks only very loosely approximate a power law distribution (Broido & Clauset, 2019) and that the myriad nuances surrounding actual network centralization dynamics remain to be understood. Regardless of any specific nuances, actual network centralization processes are 35 This example highlights the importance of point of reference when considering platform network analysis. Here, the platform is the Google search engine, while webpages/websites (i.e., the WWW) and users are the components. The connections are webpages/websites browsed by users as facilitated by the Google search engine. 84 generally subject to tempering based on structural limits and constraints (D'Souza et al., 2007)36. Therefore, while a platform may configure to encourage the emergence of a centralized network structure, the multitude of environmental dynamics and internal structural limitations will generally dampen centralization. Because platform networks’ internal and external dynamics can coalesce in a variety of ways, the degree of activity centralization will also vary from moment to moment. Higher centralization suggests greater momentary exploitation of hubs and their connective efficiencies. In contrast, lower centralization indicates a platform’s diminished capacity to organize components around a hub-centric structure at that given moment. In essence, platform networks centralize when they are configured to effectively appropriate hubs—while buffering from external pressures (e.g., hub loss). Because centralization occurs when platforms successfully identify and curate interactions around “star” components which can generate positive network flow (e.g., by anchoring component recommendations off of popular “star” components), a momentary platform configuration that achieves greater activity centralization can be viewed as providing more robust organization for subsequent activity: H2: Network centralization is positively related to activity growth. 36 Although tapering preferential attachment can be considered a general network feature, the sources of centralization decay are likely highly contextualized. In other words, while complex networks in general follow a tapered power law distribution, the reasons behind these structural constraints to centralization are likely context specific. 85 Clustering Clustering identifies the extent to which a network exhibits communities, or subgroups. Topologically, clustering reflects the network composition of interconnected components. Being interconnected means that all components are connected to all other components in the sub network. Topologically, a cluster forms when all components in a subnetwork are interconnected. A cluster consists of at least three components that are all connected to each other. Clustering can result from a variety of structural properties, including the context of the interactions mediated by the platform. Figure 3-7 illustrates the difference between networks with high versus low clustering, given identical levels of size and activity. Figure 3-7: High versus Low Network Clustering High Clustering Low Clustering Clustering37 is consequential to networks in several ways. Clustering is associated with structural closure, cohesion, and embeddedness—concepts that have a rich history in organizational theory (Borgatti & Foster, 2003; Granovetter, 1985). A classic tradeoff associated with structural closure in social settings is increased cohesion but also constraint (Burt, 1992; 37 Also referred to as transitivity. 86 Coleman, 1988; Gargiulo & Benassi, 2000). For example, cooperation arises as social capital forms and attaches individual actors to a community, orienting activity through cohesion-based processes (e.g., trust, commitment, norms and codes, etc.). In this way, clustering develops interaction and search efficiencies (e.g., Watts & Strogatz, 1998) within communities. These same network properties can also tie actors to their communities, creating inertia and rigidity; and deterring actors from departing for external alternatives (e.g., Uzzi, 1997). In essence, a structural closure paradox emerges: while generative of localized efficiencies, clustering can also constrain components to the community. Such closure can manifest in a variety of ways. Community membership can induce actor-specific network effects, or local bias (Lee et al., 2006), drawing actors to otherwise less appealing platforms. Lee, Lee, and Lee (2006) draw on the telecommunications example of network-based calling plans, whereby subscribers specify a group of phone numbers to call at discounted rates—so long as they subscribed to the same provider (p. 1839). Exploiting local bias allowed smaller carriers to gain market share by attracting, embedding, and locking in subscribers to their platforms on the basis of their social groups. Actors that interact on platforms through communities can realize multifaceted embedding processes. Such actors acquire value through activity on the platform as well as through community-based activity, but also through the potentially contextualized interaction that platforms offer communities. In other words, community interaction on platforms can deliver synergistic value which exceeds that delivered by platform activity and community activity distinctly. For example, gaming platforms offer leisure value while spending time with friends offers social value—social gaming, which combines both aspects, can offer a “complex weave of interactions and structures that go over and beyond the gaming itself” (Eklund, 2015). 87 Clustered activity (i.e., activity organized in clusters) is likely to be more entrenched than transactive actor-to-market forms of platform activity. In addition to further motivating actor-to-group momentum, clustering can also embed through a group-to-actor pull. When platform activity is community contextualized, individual actors are further embedded to the platform through their group affiliations. For example, Ducheneaut, Yee, Nickell and Moore’s (2006) online gaming study found that individuals who were members of player associations (“guilds”) spent significantly more time gaming than those who were not, due in part to social pressures such as obliging to organized events on the gaming platform. At the individual level, clustering can generate embeddedness through a stronger community based “pull” by offering more efficient, distinctive (i.e., non-substitutable), and normative expectations (cf. Barker, 1993) around platform participation. Clustered activity topologies suggest community cohesion, which can embed actors to a platform, and in turn induce network level resilience (capacity to absorb disturbance). These community effects generate network resilience by offering distinct platform interactions as well as generating a group-based pull to the platform. Because clustering occurs when platforms successfully identify and curate interactions around component communities, which can generate positive network resilience, a momentary platform configuration that achieves greater activity clustering can be viewed as providing more robust organization for subsequent activity: H3: Network clustering is positively related to activity growth. 88 Centralized Clustering In addition to clustering’s general impact on localized efficiencies and resilience, recent research across scholarly disciplines is increasingly identifying and validating the global efficiencies and resilience granted via hub-centric clustering. In other words, when networks realize clustering among highly centralized nodes—also known as rich clubs (Shi & Mondragon, 2004)—structural benefits accrue at the network level. These structural benefits can be illustrated by contrasting a network with clustering among high centrality nodes to a network with clustering among low centrality nodes, as illustrated in Figure 3-8, below. Figure 3-8: High Centrality “Rich Club” Clustering versus Low Centrality “Poor Clique” Clustering High Centrality “Rich Club” Clustering Low Centrality “Poor Clique” Clustering Figure 3-8 highlights the difference between clustering across high centrality components (thereby forming a “rich club”) versus exclusively low centrality components (forming a “poor 89 clique”)38. In both examples, three links are added to form four clusters—with each cluster consisting of three interconnected components. The difference in link placement illustrates a rich club’s asymmetric impact on network resilience and efficiency. In aggregate, when networks realize clustering among higher centrality components, overall network density and resilience improve; above and beyond the independent impacts of network centralization and clustering. Topological representations of clustering among centralized nodes are particularized across disciplines and contexts in various forms (e.g., Bascompte et al., 2003; Davis et al., 2003; Shi & Mondragon, 2004). Resiliency improvements are immediately apparent: where losing any of the original three central links would fragment the network, clustering among the most central components (i.e., forming a rich club) constructs a dense centralized hub consisting of multiple components. Losing any two of the club’s links is inconsequential to the network’s structural integrity, and three specifically targeted link removals would be required to splinter the network. The distinct communities are connected through multiple channels, generating redundancies to buffer from systemic and targeted perturbations. Centralized clustering’s impact on density is less obvious on a small scale. However, the typological benefits increase by orders of magnitude with network size, and as the distance bridged between hubs increases (Bertolero et al., 2017). When clustering manifests among otherwise distant hubs, wider structural holes (e.g., Burt, 1992) are bridged in the network. As rich clubs form across otherwise greater distances, the density of the entire network improves 38 For illustrative purposes, I use a simple tree graph with two different clusters to show the difference between clustering among high centrality components and low centrality components. For simplicity, I contrast two distinct clusters, or sub-groups. However, it is important to emphasize that centralized clustering is a network level characteristic that refers to the presence of such high centrality clusters. The network level effects are more apparent, but more difficult to illustrate graphically, when considering a large-scale network. As a network level property, the presence of centralized clustering has significance above and beyond clustering and centralization. 90 significantly because hubs essentially act as ports into distinct communities. When hub cluster(s) form a network substructure, flow efficiencies effectively “shrink” the network so that otherwise distant communities are more accessible through their adjoining hub(s). Centralized clustering engenders effects above and beyond the localized resilience and efficiencies granted by clustering in general. When clustering occurs among higher centrality components, the resilience and efficiency improvements scale exponentially. Clustering’s second-order benefits manifest in proportion to the number of components that interact with the cluster’s constituent components. Therefore, when a cluster’s components consist of high centrality hubs, transitivity improvements emerge across the set of second degree components that are connected to this hub cluster. These improvements increase exponentially with the centrality of the clustered hub components. Hubs densify a network by concentrating connections. When multiple hubs are interconnected, transitivity improvements extend across components that are directly and indirectly connected to the clustered hub substructure. Centralized clustering can also generate a third, less obvious, network benefit by concentrating hubs in their ecological role as generalists39. The concept of ecological niche expansion from concentrating generalists echoes across disciplines and contexts in various forms. For instance, there has been a surge of recent research in bioecology focusing on the structure of mutualistic bipartite networks (i.e., made up of two “sides”). These studies find that many diverse mutualistic ecosystems exhibit a nested architecture for interspecies interaction. To be nested, a network must consist of a core group of generalists all interacting with each other, and with extreme specialists interacting only with generalist species (Nielsen & Bascompte, 2007). Nestedness has been found to improve biodiversity (Bascompte et al., 2003; Bastolla et 39 Note that high centrality actors, though likely, are not necessarily generalists (e.g., Carroll, 1985). 91 al., 2009); though precise mechanisms are still under debate (cf. James et al., 2012; Saavedra & Stouffer, 2013). Nestedness originates from bioecology, but—like many network ecological concepts—finds its way to the industrial organizational context (e.g., Saavedra et al., 2009; Saavedra et al., 2011; Uzzi, 1997). More recent studies highlight nestedness’ structural benefits also manifest in industrial settings. For example, Brehm and Layton (2021) find that nestedness can improve the reuse of materials and energy in eco-industrial networks. On the same vein, Chatterjee, Brehm, and Layton (2021) suggest that nestedness may be pivotal in developing “industrial symbiosis” which provides an avenue for ecologically sustainable and resilient economic growth. Remarkably, a similar dynamic was actively studied in the organizational theory literature leading up to the turn of the millennia. Organizational ecology’s resource partitioning theory (Carroll, 1985) suggests that a concentration of multiple generalists expands the overall resource space for specialists (Carroll & Swaminathan, 2000; Peli & Nooteboom, 1999), improving overall population density and diversity. The theory continues to evolve in it’s contemporary form (Hannan et al., 2007), elaborating on categorical innovation (Rao et al., 2005) and emergence (Weber et al., 2008). The research suggests that traversing categorical boundaries asymmetrically impacts actors according to factors such as status, and the strength of the boundaries themselves. For example, Rao, Monin, and Durand’s (2005) French gastronomy study found that higher status actors had more capacity to traverse and weaken boundaries; and that weak boundary regimes can even stimulate categorical blending (p. 985). Imagine the same dynamics unfolding in a platform context: it could be a collaboration between two high profile content producers from different genres, or a bundle of two popular products from different yet complimentary 92 categories. Multiple connected high centrality components may very well signify the ecological scaffolding for weak categorical boundaries; in essence that there is transmission between a set of communities through their respective hubs. Such structure may signal the emergence of additional categorical niches (e.g., Weber et al., 2008). Centralized clustering accompanies distinct topological implications above and beyond centralization and clustering. While clustering generates intracommunity efficiencies, centralized clustering produces intercommunity efficiencies (i.e., by concentrating connections among components that are highly connected with other components). Where centralization generates network level efficiencies at the risk of increased fragility, centralized clustering induces network efficiencies with increased resilience. Furthermore, centralized clustering may well indicate network-expanding structural configurations manifesting from weakening boundaries between subnetworks (i.e., communities) within the platform network. Taken together, the presence of centralized clustering is conduscive to overall activity growth: H4: Network centralized clustering is positively related to activity growth. Cross-functionality Platforms’ component compositions can vary. At a broad level, platforms can be understood as multisided markets that create value through efficient matching of actors. Actors can be categorized as belonging to at least one “side” of a platform-mediated market. An archetypal platform configuration is one where there are two sides which are distinctly represented by two sets of actors; one on the supply side (i.e., complementors) and another on the demand side (i.e., users/consumers). These clearly delineated two-sided markets inform the 93 bulk of the industrial economics literature on platform dynamics (e.g., Rochet & Tirole, 2003; Rysman, 2009). However, many platforms exist where a given actor will generate activity attributable to multiple sides (see Afuah, 2013). Network cross-functionality—the degree of functional overlap among components—remains largely unacknowledged and unincorporated in current platform conceptualizations. Depending on the platform, actors may participate along multiple sides as opposed to being constricted to performing only a single side’s functions (e.g., producing versus consuming). Actors interact within the structural features of the platform, producing discernible activity patterns. Motifs can provide a basis for identifying the functional composition of a platform’s underlying population. In a directed network structure, nodes can be construed as sending (i.e., initiating) and receiving (i.e., fulfilling) interactions from other nodes. Therefore, nodes that either send exclusively or receive exclusively can be categorized as belonging to one side. Conversely, nodes that both send and receive to some degree belong to both sides. Figure 3-9 illustrates the four base motifs comprising any directed network’s topology: Figure 3-9: Network Flow Base Motifs These motifs are the foundational elements of any directed network’s flow structure. In other words, all other motifs involving more than two directed ties derive from at least one of the four unique base motifs. The reciprocal and sequential motifs represent a focal node engaging in 94 activity belonging to two sides of a platform interaction whereas the two-in and two-out motifs represent a component that is engaging in one form of activity with two other distinct components. A single actor can account for a profile composed of several—even all—base motifs. Analyzing the proportions of different network flow motifs can provide a means of measuring the broad functional overlap of a platform network. Platform networks with actors producing exclusively one-way activity flows (i.e., two-in and two-out) are likely to be less resilient than platforms with functional overlap among actors. As ecosystem participants, niche theory suggests that actors operating under a single functional role will continue to interface with a particular market through a given platform to the extent that they continue to realize positive fitness (i.e., value) in that role. Actors that no longer appropriate value in their singular role on the platform no longer have reason to maintain participation. Conversely, actors that interact on a platform in a multitude of functional capacities (i.e., multiple sides) are buffered from platform exit so long as they realize value from at least one of their functional roles. Niche theory holds that a population of actors that can diversify its position in the broader environment benefit from competitive buffering. Thus, actors operating in multiple roles form a multiplex relationship with the platform, thereby contributing resilience to perturbations (e.g., competitive shifts) at the network level. Systemic perturbations can diminish the viability of a particular platform side. Network cross-functionality fosters contingencies; improving network resilience and recoverability. Actors that no longer viably perform on one side can remain active on an alternative capacity—and possibly even renew future viability on the disrupted platform side. Conversely, actors in singular roles that exit the platform following fitness loss are less likely to continue to attend to the state of the platform; while reintegration is likely much lower and preceded with substantive 95 search costs. For example, suppose a food delivery platform launches in a particular city. As the platform develops its network of takeout users, restaurants, and couriers, it may realize network dynamics that can affect the platform experience for select groups of actors (e.g., unbalanced scaling). Couriers that are not given sufficient delivery opportunities, perhaps due to high competition or low demand, may exit the platform. However, if they are also takeout users, they may be able better monitor signals in the platform environment suggestive of renewed fitness as a courier (e.g., increased demand from a boom in neighbourhood restaurant listings, slow delivery times, limited time incentives, etc.). Depending on the context, the perturbation defense and actor retention benefits garnered by network cross-functionality can be less costly and more strategically robust than attracting new actors. Perturbations can develop from exogenous sources such as opportune openings in competing platforms. Even if only one side of actors disproportionately migrates to an adjacent platform, other sides in the focal platform can destabilize through the resulting diminished network effects. If actors occupy a singular role (i.e., side), such disruptions can initiate a cascading punctuated decline whereby network effects are disheveled—in turn causing dependent side(s) to unsubscribe from the platform. The resulting vicious cycle of platform decline can be reversed to the extent that new actors sufficiently replenish the lost ones. However, new actors must surmount search costs proportionate to the number of similar platform alternatives in the local environment. Network cross-functionality (i.e., actor functional overlap) can generate a reserve pool of components to buffer and potentially replenish a disrupted platform side. A local pool of latent actors (for a particular side) are not exposed to the additional search costs that external actors 96 are. Therefore, cross-functionality grants network redundancy benefits that can be particularly advantageous in attenuating perturbations on platform activity. Cross-functionality likely also makes platform scaling more efficient and smoothed. As platforms scale, same-side and cross-side network effect dynamics are impacted. Cross-side network effects are generally positive, referring to the attractiveness of the platform to one platform side due to the agglomeration of the other side—which the first side seeks to interact with. Actors that operate on multiple sides can more efficiently fill openings created from cross-side network effects. Same-side network effects can be positive (mutualistic) or negative (competitive). Actors that decline in competitiveness in one role can fall back on other roles and still remain active on the platform. As a result of this redundancy-granted resilience, functional overlap smooths out actors’ platform specific fitness profiles compared to the binary viability prospects that single function actors face. Therefore, platform networks with greater cross-functionality should realize more resilient activity growth in general: H5: The proportion of sequential and reciprocal activity motifs is positively related to activity growth. 97 CHAPTER 4: METHODS Ethereum Blockchain Ethereum, a current distributed trust technology (Seidel, 2018) manifestation, provides an operating system for distributed smart contracts. Smart contracts are readable and immutable computational scripts that contain functions allowing actors to initiate and realize transactions through. These smart contracts are deployed onto, interfaced through, and executed via the Ethereum virtual machine (EVM) environment. Actors expend diminutive amounts of Ethereum’s primary currency—ether—in order to add smart contract function calls to the queue of transactions to be verified (i.e., processed). The Ethereum blockchain is maintained and new transactions authenticated via a consensus algorithm whereby participants are rewarded with ether. The exact mechanics of the Ethereum consensus algorithm, and its evolution, are beyond the scope of this chapter; however, abundant information can be found in the public domain. Smart contracts are the technical cores of digital platform applications40. As with most technological assemblies, actors seldom interface directly with a particular element but rather with an encapsulation of the system. However, a primary feature of the decentralized ledgers and databases underlying these applications is that they are distributed, immutable, and transparent. Indeed, these are the very characteristics of smart contracts, and the transactions that they mediate, which classifies them as a distributed trust technology. These same characteristics also lend themselves unprecedentedly well to studying platforms from a network perspective. In essence, the Ethereum blockchain is a detailed ledger of smart contract based digital platforms and the transactions they mediate. Each transaction is publicly accessible and 40 Blockchain based applications are generally referred to as decentralized applications, or “dApps.” 98 irreversible. Transactions can include the creation of addresses (representing actors), contract function calls (representing transactions), and the creation of smart contracts (representing platforms). Addresses interact on a platform through contract function calls. All articles—contracts, transactions, and accounts—have associated identifiers. Transactions have transaction hashes, while contracts and accounts have addresses. Some contracts only accept and operate by means of their exclusive tokens while others operate using ether. Groups of transactions are verified, stored, and sequentially chained together in blocks (hence, “block-chain”). Contracts represent platforms on Ethereum41. There were over 78,000 verified Ethereum contracts by 2020 (Ethereum Daily Verified Contracts Chart, n.d.) amidst millions of unverified contracts. Many unverified contracts do not facilitate any transactions between their inception and the last point of data collection. Some contracts contain coding errors, or are copies of other contracts, but remain on the Ethereum blockchain after being deployed due to its immutability. Transaction volumes are highly skewed, with the highest volume contracts accounting for a significantly large portion of overall volume. Table 4-1 provides an example of transaction volumes for the top 10 highest volume Ethereum contracts from blocks 4,370,000 (approximately October 16, 2017) to 9,200,000 (approximately January 1, 2020): 41 Although Ethereum itself can be construed as a platform (of platforms), I analyse contracts deployed onto Ethereum as platforms (not as components). It is also worthwhile to emphasize the importance of clearly defining the platform(s) being analysed, particularly as many platforms can also be construed as components; and vice versa. 99 Table 4-1: Top 10 Ethereum (Metropolis) Addresses by Transaction Volume (10/16/2017-1/1/2020)42 Address Volume Name 0xdac17f958d2ee523a2206206994597c13d831ec7 14939515 Tether 0x174bfa6600bf90c885c7c01c7031389ed1461ab9 8947028 More Gold Coin 0x0e3a2a1f2146d86a604adc220b4967a898d7fe0743 7231659 Gods Unchained (Batch Wrapper) 0x629cdec6acc980ebeebea9e5003bcd44db9fc5ce 6680552 Gods Unchained (Cards) 0x58b6a8a3302369daec383334672404ee733ab239 5563519 LivePeer 0x03cb0021808442ad5efb61197966aef72a1def96 5349547 CoToken 0x06012c8cf97bead5deae237070f9587f8e7a266d 4809370 Cryptokitties 0xc02aaa39b223fe8d0a0e5c4f27ead9083c756cc2 3294075 Wrapped Ether 0x89d24a6b4ccb1b6faa2625fe562bdd9a23260359 2935593 Sai Stablecoin 0xf230b790e05390fc8295f4d3f60332c93bed42e2 2750537 Tronix Data This dissertation’s analysis timeframe spans blocks 4,370,000 to 9,200,000; corresponding to Ethereum’s third developmental phase, known as Metropolis. Metropolis consists of three distinct upgrades: Byzantine (implemented at block 4,370,000), Constantinople (implemented at block 7,280,000), and Istanbul (implemented at block 9,069,000). Each upgrade implements a set of incremental Ethereum Improvement Proposals (EIPs) while broader phase 42 Source: Google BigQuery custom table. 43 0x0e3a2a1f2146d86a604adc220b4967a898d7fe07 (GODS Unchained CARD token) is excluded from analysis due to not having a minimum six weeks of consecutive activity; a requirement relevant to this dissertation’s analytical approach. 100 transitions (e.g., into—and out of—Metropolis) bring about foundational change to the Ethereum protocol. For example, Metropolis’ scalability improvements contributed to a significant shift in transaction volumes. As a result, the previous phase’s maximum daily transaction levels barely reach Metropolis’ minimum daily transaction volumes (Ethereum Daily Transactions Chart, n.d.). Therefore, the analysis timeframe encompasses a single complete phase because developmental phases represent distinct environmental regimes. This dissertation’s initial analysis dataset consists of the 200 highest transaction volume contracts throughout Ethereum’s Metropolis phase44. These 200 contracts account for over 18% of Ethereum’s Metropolis transaction volume (Ethereum Daily Transactions Chart, n.d.). I focus on the Metropolis phase because it possesses the greatest transaction volume and variety of all completed Ethereum phases, by far. I obtained transaction data for each of the contracts through Covalent’s45 blockchain database. Empirically, blockchain data presents an exceptional and promising frontier for platforms research as well as network science for at least three complementary reasons. First, the data granularity is unprecedented. Transaction level data is the lowest unit of analysis, providing high resolution data as well as flexibility around level of analysis. Second, the data is complete. In addition to alleviating typical data missingness concerns, having complete data in a large network context is rare and especially advantageous. Missingness in network data is 44 This dissertation’s sampling approach inherits a methodological “Achille’s Heel” in that it may raise concerns around sampling on the dependent variable. While valid, the unique and exceptional empirical opportunity offered through the Ethereum blockchain data eclipses these concerns. Moreover, any sampling bias is aligned with the theoretical and practical bias contextualizing contemporary platform analysis. That is, this dissertation’s theoretical perspective inherently orients towards sufficiently scaled platforms with higher activity volumes. 45 Covalenthq.com indexes blockchain transactions, and maintains a copy of the Ethereum blockchain in structured format. Special thanks to Ganesh Swami for providing high volume access to the data; and to Chris Rowell for connecting us. 101 consequential beyond the relatively linear impacts of more conventional subject-by-subject analyses because missing network components can not only impact the sample but also the network structure under examination (Huisman, 2009). When a component is missing, so are all of its connections; which can drastically misrepresent the broader network. Third, the data provides a temporal dimension that is aligned with this dissertation’s emphasis on network dynamics. In parallel to the institutionally generative potential of blockchain (Allen et al., 2020), I leverage the technology to empirically analyze complete platform network data; an opportunity otherwise not available. The data spans from block 4,370,000 to 9,200,000; or from roughly October 17, 2017 to January 1, 2020. I structure the data in roughly weekly increments, or 604,800 second spans46, yielding 112 time periods. Contracts can initialize and terminate within the analysis timeframe. Therefore, each contract can yield at most 112 complete time periods because not all contracts or are active throughout the entire analysis timeframe. A timestamp accompanies each transaction. The earliest timestamp for block 4,370,000 is 1508156531. Therefore, the first analysis time period constitutes transactions taking place from after timestamp 1508156530 up to and including 1508761330; and the second time period includes transactions from after 1508761330 to 1509366130. Figure 4-1 illustrates the transaction volumes of the top ten contracts with over six weeks of consecutive activity47 throughout the various analysis time periods corresponding to Ethereum’s Metropolis phase. 46 Determined as 3600 seconds/hour * 24 hours/day * 7 days/ week. 47 0x0e3a2a1f2146d86a604adc220b4967a898d7fe07 (GODS Unchained CARD token) is excluded due to not meeting this criteria, which is relevant to this dissertation’s analytical approach. 102 Figure 4-1: Weekly Activity of the 10 Highest Volume Ethereum Metropolis Contracts One key advantage of blockchain data is that only completed transactions are stored. For example, if a platform facilitates component matching involving a search process, only completed transactions are recorded on the blockchain—not activity around the processes that led up to it (e.g., search). Therefore, using completed transaction data exclusively measures “core” platform activity. Another key feature of completed blockchain activity is that each transaction requires a transaction fee to be paid (Ethereum’s is called “gas”). This feature regulates the number of transactions processed at a given time, and disincentivizes trivial activity (i.e., spam). More complex functions which pass through multiple methods and potentially multiple smart contracts will carry a higher fee. 103 Statistical Software I use Stata and R to prepare and analyze the data. While Stata acted as the primary analysis and data preparation software, numerous network measures were either readily available or more easily calculated in R due to its extensive network-based library of packages and features. Due to this project’s considerable data volume and processing requirements, all data preparation and analysis were computed using Canada’s national advanced research computing (ARC) platform via Compute Canada48. As well, access to the MISR@UBC research server was provided for auxiliary computing49. Measures Dependent variable Activity is coded as the number of transactions attributed to the contract during a given time period50. I natural log transform this variable to interpret analysis results in percentage change (i.e., growth) terms. In addition to providing a more theoretically aligned interpretation, log transforming activity provides statistical modeling advantages such as reducing heteroscedasticity (i.e., stabilizing variance), thereby providing a more linearized signal of growth patterns and reducing noise (Singer & Willett, 2003). Log transforming activity also helps to place nonlinear growth trajectories into the context of linear growth modeling (e.g., 48 Currently administered by the Digital Research Alliance of Canada, following a transition in April 2022. 49 A huge thank you to Gene Moo Lee for facilitating access to this wonderful resource. 50 Activity includes all function calls; not just transfer()—which is used exclusively to develop independent variables around activity structure. 104 Colder et al., 2001). Figure 4-2 illustrates the weekly natural log transformed activity for the top 10 contracts with over six weeks of consecutive activity. Figure 4-2: Weekly Activity of the 10 Highest Volume Ethereum Metropolis Contracts (Natural Log Transformed) Independent variables Several independent variables make use of address’ degree centrality. The degree centrality of a given address, i, is simply the sum of the number of other addresses connected to it: 𝐶ௗ(𝑖) = ෍ൣ𝑒௜௝൧௡௝ୀଵ 105 where j identifies all addresses (i.e., 1 to n) in the network. Therefore, 𝐶ௗ(𝑖), captures the number of transactions involving a given address, i. Connectance is coded as the number of realized connections during a given time period. A realized connection occurs when one address transacts with another address through the contract (i.e., the platform). Incoming, outgoing, and reciprocal connections between a pair of addresses are considered equally. An address with an outgoing connection to another address but no incoming connection from the same address is calculated as having one realized connection. The same pair would also be calculated as having one realized connection even if the second address reciprocated the connection, as this dissertation opts for a simpler undirected network approach for more basic network properties such as connectance. Doing so represents a more conservative and accessible approach while relaxing assumptions about the structure of platforms (i.e., contracts) being analysed, as well as the degree to which components can interact. Moreover, cross-functionality—which is measured in this dissertation—accounts for the latter. Taking a directed network approach to connectance risks unnecessary redundancy at lower resolution given cross-functionality’s presence. Therefore, given undirected data, network connectance can be calculated as: 𝐶஻ =12෍ 𝐶ௗ(𝑖)௡௜ୀଵ where CB is half the sum of each address’ degree centrality. Given undirected data, the original sum should be halved due to double counting of each address’ degree centrality (i.e., each 𝑒௜௝ will also be represented as 𝑒௝௜). 106 It is worthwhile to address alternative approaches to measuring connectance. Although connectance is oftentimes calculated as a proportion of the maximum connectivity, I use the number of realized connections due to two reasons. First, due to the exponential relationship between network size and connectivity, measuring connectance as a proportion of maximum connectivity would mathematically place connectance on an exponentially-decreasing size-dependent scale. Therefore, all models will control for size. Due to this modeling approach, using realized connections will decompose the effect of connectance above and beyond size. Second, while fields such as ecology tend to opt for the proportion-based version, this dissertation’s focus on network growth dynamics does not suit the more stable network size assumptions (e.g., when analyzing interspecies food webs) preceding proportion-based connectance measures. Finally, connectance is natural-log transformed to linearize and accommodate model results interpretation (Willett & Bub, 2014). Centralization is coded using the Freeman network centralization coefficient (Freeman, 1978): 𝐶஽ =∑ 𝐶ௗ(𝑚𝑎𝑥) − 𝐶ௗ(𝑖)௡௜ୀଵ(𝑛 − 1)(𝑛 − 2) where Cd(i) is the degree centrality—the number of connections with all other unique addresses in the network—of address i, and Cd(max) is the degree centrality of the address with the highest degree centrality in the network for a given time period. Degree centrality is calculated from established connections as opposed to interaction frequency. Therefore, multiple transactions between two addresses will be counted as a single connection. The total number of addresses is represented as n. The denominator represents the maximum centralization score of a network given the same number of addresses, n. The most centralized network occurs when all 107 connections are with a single address only (i.e., “star form”). If the network is structured as a star, then the numerator will be equivalent to the denominator—yielding the highest centralization score of 1. Therefore, another way of interpreting the centralization measure is as how close it is to a fully centralized star form network. Conversely, all addresses having the exact same degree centrality will result in a network centralization of 0. Network centralization can range from 0 (lowest) to 1 (highest). Clustering is coded following the Watts and Strogatz approach (Watts & Strogatz, 1998). Calculating the clustering coefficient for a given time period involves multiple steps and multiple components. First, all active addresses during the time period have their local clustering coefficients determined as: 𝐶௟(𝑖) =2|{𝑒௝௞ ∶ 𝑣௝ , 𝑣௞ 𝜖 𝑁௜ ˄ 𝑒௝௞ 𝜖 𝐸}|𝑘௜(𝑘௜ − 1) where the neighbourhood, Ni, of vi (address i) follows the definition: 𝑁௜ = {𝑣௝ ∶ 𝑒௜௝ 𝜖 𝐸 ˅ 𝑒௝௜ 𝜖 𝐸} where i < j < k (to offset double-counting), and such that v represents addresses and e represents transactions between addresses. Therefore, each neighbourhood of an address, Ni, represents a set ({…}) of addresses such that (vj :) a transaction from address i to address j (eij), or (˅) from address j to address i (eji) exists within the set of transactions (E). In other words, Ni is the set of addresses that a particular address i realizes a transaction with during the given time period. The set of addresses is non-repeating: an address is included once per focal address set regardless of the number and direction of transactions in the given time period. 108 The local clustering coefficient of an address, Cl(i), can be viewed in terms of two constituents. Because its constituents are derived from Ni, I first address the denominator, 𝑘௜(𝑘௜ − 1)/2. Specifically, ki is the number of elements in the set Ni (i.e., 𝑘௜ = | Ni | ). Therefore, the denominator represents the maximally connected subgraph of the set of addresses, Ni. In the event of undirected or direction-indiscriminate connections, there can be only one connection between addresses—hence the divisor of 2. In other words, in a set of 𝑘௜ nodes, the maximum number of connections is 𝑘௜(𝑘௜ − 1)/2 The numerator, |{𝑒௝௞ ∶ 𝑣௝ , 𝑣௞ 𝜖 𝑁௜ ˄ 𝑒௝௞ 𝜖 𝐸}|, represents the count of a set (|{…}|) of transactions such that (𝑒௝௞ ∶) the addresses are elements in the set of addresses connected to address i (𝑣௝ , 𝑣௞ 𝜖 𝑁௜) and (˄) the transactions are elements in the set of realized transactions (𝑒௝௞ 𝜖 𝐸). In other words, the numerator represents the number of realized connections between addresses that have transacted with address i during the given time period. The local clustering coefficient of an address, Cl(i), represents the proportion of realized connections of addresses connected to a focal address, i, during the given time period. To measure the degree of clustering in a given contract, I take the mean of all (i.e., n) local clustering coefficients using the formula: 𝐶̅ =1𝑛෍ 𝐶௟(𝑖)௡௜ୀଵ Centralized clustering follows Colizza et al. (2006). To pick up the presence of centralized clustering, I first calculate the rich club coefficient for a given network using a minimum degree cutoff, k, as: 109 𝛷(𝑘) =2𝑇வ௞𝐴வ௞(𝐴வ௞ − 1) where T>k is the number of unique51 transactions between components with more than k connections, and A>k is the number of addresses with more than k connections. Note that the denominator, 𝐴வ௞(𝐴வ௞ − 1)/2, represents the maximum number of undirected connections for the sub-network of addresses with greater than k connections. For directed connections, the 2 divisor is dropped52. Therefore, Φ(k) measures the “completeness” of a subnetwork consisting of addresses with more than k connections. Cross-functionality is coded as the total number of sequential motifs divided by the total number of two-in and two-out motifs for a given time period53. Reciprocal motifs are not utilized in calculating cross-functionality due to the fact that some contracts produce transactions whereby settlement of a single transaction results in a reciprocal motif. For example, a market matching platform can construct a transaction such that residual or ancillary amounts (i.e., “change” or receipts) are returned to the transaction initiator, resulting in a reciprocal motif. 51 Though outside the scope of this dissertation, I discuss the opportunity to incorporate weighting in Chapter 6: Discussion and Conclusion. 52 This dissertation does not elaborate on directed connections with respect to centralized clustering, but recognizes its potential in providing an additional layer of detail to platform network analysis. I discuss future opportunities in Chapter 6: Discussion and Conclusion. 53 It is worthwhile to acknowledge here that motifs retain transaction directionality. None of the other network variables are constructed with this level of resolution; and omit the direction of transactions. Cross-functionality, which is unique to this dissertation, demonstrates the capability and flexibility of motifs in operationalizing structural phenomena. Motifs are substructures that can be adapted to context to elicit broader structures and structural properties. Just as cross-functionality is a pertinent topic in the platforms literature (i.e., the extent to which platform participants exhibit “multisiding” behaviour), other organizational studies have also leveraged network motifs to identify network configurations that are more context-specific and microfoundational. For example, Lomi and Pattison (2006) leverage network motifs to study local dependence structures and the ways they extend across multiple networks in a supply chain. 110 While some reciprocal motifs will indeed be legitimate (i.e., distinctly separate transactions), I opt for a more conservative approach by excluding reciprocal motifs from calculating cross-functionality. Therefore, when contracts’ transactions are decomposed into all single-address-connected motifs, three quantities based on distinct motif sets are generated for a given contract: 𝐹ଶ௜௡ = ෍ห൛𝑚௜௝௞ ∶ 𝑒௝௜ , 𝑒௞௜ ϵ 𝐸ൟห , 𝑖. 𝑒. , { 𝑗 → 𝑖 ← 𝑘 }௡௜ୀଵ 𝐹ଶ௢௨௧ = ෍ห൛𝑚௜௝௞ ∶ 𝑒௜௝ , 𝑒௜௞ ϵ 𝐸ൟห , 𝑖. 𝑒. , { 𝑗 ← 𝑖 → 𝑘 } ௡௜ୀଵ 𝐹௦௘௤ = ෍ |{𝑚௜௝௞ ∶ 𝑒௝௜ , 𝑒௜௞ ϵ 𝐸}|௡௜ୀଵ, 𝑖. 𝑒. , { 𝑗 → 𝑖 → 𝑘 } where i > j > k in terms of identifier to avoid repeating identifier combinations and where each quantity is a summation of the count of a set of (Σ|{…}|) motifs involving three nodes, i, j, and k, such that (𝑚௜௝௞ :) two directed transactions are drawn from a set of directed transactions, E. Excluding the reciprocal motif, the three quantities capture the motif counts corresponding to the full set of two directed transactions connected by a common node. Therefore, the final functional overlap for a contract during a given time period is the proportion of sequential motifs to two-in and two-out motifs: 𝑂௜ =𝐹௦௘௤𝐹ଶ௜௡ + 𝐹ଶ௢௨௧ Size is coded as the number of unique addresses that hold an exclusive token or, in the case of contracts that use ether, the number of unique addresses interacting with the contract during a 111 given time period. Size is natural-log transformed to linearize and accommodate model results interpretation. Contract Fixed Effects are controlled for by dummy coding each contract. Controlling for contract fixed effects better isolates activity organization effects from contract-specific growth effects during modeling and analysis (Allison, 2009). Including contract fixed effects focuses on within-group variation while removing omitted variable bias associated with between-group variation. Contract fixed effects are a particularly important part of this dissertation’s analytical strategy, as platforms differ in their inherent topological tendencies. Therefore, network structural impacts on activity growth should be modeled according to within-contract dynamics. Note that some Ethereum-based platforms are designed using multiple smart contracts. Such platforms tend to be more complex. However, it is safe to assume that such designs are well-motivated as efficiency is strongly incentivized; particularly for the top 200 most active contracts. Smart contracts prioritize efficiency, as uneconomical code will incur nontrivial transaction fees; and is ultimately less desirable for all stakeholders. In such cases, the full picture of such a platform is partitioned across multiple contracts—some of which may not be present in the analytical sample (i.e., not in the top 200 most active contracts). Analyzing such contracts is acceptable for the purposes of this dissertation several reasons. First, not having the fully integrated platform activity topology results in conservative analyses as a larger, higher activity, network structure is forgone for multiple smaller ones. Second, the activity in one contract will likely be connected to another but in a modular and meaningfully delineated way (e.g., one contract may organize components to facilitate 112 innovation activity, which in turn inventories components for downstream market interactions organized on another contract). Third, being able to access multiple contracts belonging to the same platform enables a path for more detailed analyses of platforms’ multiplex activity54. Time Period Fixed Effects are controlled for by dummy coding each starting time period. Therefore, up to 36 time periods are coded. Controlling for time period fixed effects helps to partition the activity growth and organization relationship from any period-specific impacts on activity. This control is particularly important as Ethereum’s transaction fees (i.e., “gas prices”) scale with volume, and there have been periods where this regulatory process would have dampened any otherwise organic activity growth (Ethereum Average Gas Price Chart, n.d.). Data Preparation Reducing and restructuring the data from transaction level to network-time period data involved numerous steps and extensive processing. Variables are coded throughout the data reduction process, which follows three general steps. First, I define time periods based on weekly intervals (i.e., 604,800 second increments). Total activity (the dependent variable) is calculated for each contract time period. Dividing Ethereum’s Metropolis timeframe into weekly intervals produces 112 distinct time periods. Second, I construct transaction-based networks for the set of fixed time periods and code key network variables. I define activity networks using the transfer() function. Contracts can 54 Such analysis is beyond the scope of this dissertation, though it is elaborated on in Chapter 6: Discussion and Conclusion. 113 contain many functions. However, all contracts utilize transfer(), a core function through which addresses transfer digital tokens. An initial function call can trigger an array of different function calls downstream, and eventually result in transfers. In other words, regardless of the exact functions executed, transfer() calls provide a concise reduction of contract-mediated transactions. Three fields accompany each transfer() call: (1) a “to” address, (2) a “from” address, and (3) a “value” representing the token(s) being transferred. Due to its simplicity and primacy throughout Ethereum contracts, I use transfer() transactions to construct a directed (i.e., incorporating direction) transaction network for each time period. Using the resulting transfer()-based network, I produce topological measures for each contract-time period55. Third, I wide-form the data into consecutive six-time-period rows. This dissertation’s analytical approach utilizes latent growth modeling (LGM) under a structural equation modeling (SEM) framework incorporating fixed effects. Although there is currently no definitive rule on how many time periods to incorporate for a linear growth trajectory, the recommendations of several foundational texts covering LGM converges on six periods as an optimal standard (Preacher et al., 2008, p. 12)56. To avoid oversaturation (i.e., by using all 106 potential model periods), I increment each measurement window by three periods such that each contract can encompass 36 growth curves at most: T1 (i.e., growth curve from T1-T6), to T4 (i.e., growth curve from T4 to T9), to T7 (i.e., growth curve from T7 to T12), through to T103 (i.e., growth curve from T103-T109), and finally T106 (i.e., growth curve from T106-T112). 55 It is worthwhile to mention that, although transfer() transactions act as the building block for all independent variables, each of the variables is distinct unto itself. 56 It is worthwhile to note that few empirical studies have the luxury of selecting up to six intervals. 114 I retain only rows with activity throughout six consecutive time periods57. Because networks require sufficient transactions to generate meaningful structural measurements (e.g., suppose a given contract time-period has only one single instance of activity between two addresses—measuring this observation as a perfectly connected network would be nonsensical), I further drop time periods with fewer than 50 transactions in the first time period of each row58. I emphasize here that, while growth curves are constructed using data spanning six consecutive time periods, all predictors are drawn from the first time period of each row. The final analysis dataset is then rendered using listwise deletion and comprises only observations that have non-missing values across all variables of interest59. Analysis To predict contracts’ latent activity levels, I partition, then analyze, the repeated measures data using latent growth curve modeling (LGM) within a structural equation modeling (SEM) framework. Data are segmented into weekly intervals from October 17, 2017 to October 29, 2019. Each model observation uses six sequential weekly intervals, resulting in up to 36 potential observation periods with start points seven days (i.e., 604,800 seconds) apart, from October 17, 2017 (T1) through to October 22, 2019 (T36). LGM exploits the latent variable factor estimation approach used in SEM by linearly constraining the factor loadings of the repeated activity measures to estimate a linear time- 57 Dropping 556 rows, including 5 contracts; and leaving 4075 contract-time observations across 188 contracts. 58 Dropping 538 rows, including 2 contracts; and leaving 3537 contract-time observations across 186 contracts. 59 Dropping 137 rows, including 15 contracts; and leaving 3400 contract-time observations across 171 contracts. 115 progressing slope (Preacher et al., 2008; Willett & Bub, 2014). I use the activity levels of six consecutive time intervals as factor loadings to specify the latent slope and intercept. The activity level slope factor loadings are fixed to 0, 1, 2, 3, 4, and 5 to align with the group of six respective incremental time intervals, while all activity level intercept loadings are fixed to 1. Independent variables from the first time period of the interval group are used to predict the latent activity slopes to test hypotheses60. Where conventional LGM approaches utilize repeated measures to form a growth trajectory, this dissertation adopts a repeated trajectories approach. Specifically, I layer the conventional LGM approach with a moving time window element; thereby generating a progression of growth trajectories for each contract across the 36 time periods made up of 112 seven-day intervals. In other words, a set of growth curves—themselves constructed from a series of repeated activity measures—is nested within each contract, resulting in a multilevel LGM approach. Figure 4-3 illustrates this dissertation’s LGM and specifically highlights the slope factor loadings. Multiple slopes are modeled for each contract; with each model anchored at time period i: 60 It is worthwhile to note that this dissertation’s LGM approach carries many empirical advantages; many of which result in conservative longitudinal analytical tests. Predicting a longitudinal trend spanning over multiple consecutive time periods lends itself to robust results, should any meaningful ones be found; particularly when compared to a temporal outcome measured as a singular point. Another related example is reverse causality: in this case, the possibility to argue that activity growth leads to structures. The possibility of such a relationship is well-motivated (e.g., Barabási & Albert, 1999). Indeed, this dissertation’s theoretical framework promotes a recursive relationship between activity and structure. However, the present focus remains the relationship between structure to activity. Regardless of whether the reverse relationship exists, the LGM approach is robust against reverse-causality concerns. Not only is temporal precedence incorporated, but the outcome itself is constructed using multiple measurements over an extended set of cumulative periods (e.g., as opposed to a single period, which could well be correlated to past measurements). 116 Figure 4-3: Latent Growth Curve Model with Slope Loading Scores where i is drawn from a set I = (Dion, 2000 10, …, 97, 100, 103, 106). All intercept factor loadings are constrained to 1 and all slope factor loadings are constrained to j, the difference between the activity factor component time period and i. Because multiple growth curves are constructed using activity factor components—each from six sequential time periods—let j be drawn from a set J = (Hannan & Carroll, 1992 3, 4, 5) such that a given time period takes the value i + j. Each slope is therefore constructed using six factors with loading values matching j, drawn from a set J = (Hannan & Carroll, 1992 3, 4, 5). Slope factor loadings are highlighted in blue. To isolate activity organization effects from network size and extraneous variables, I use the dummy-variable approach to fixed effects modeling by including a variable for each contract and time period. During modeling, I include all contract dummies except for an average volume 117 contract61 and time period62 which were selected as references. By controlling for extraneous variation across time and contracts, endogenous network structural growth dynamics can be isolated from network size effects without being confounded by any particular exogenous effects—many of which are still not understood, or even identified, in the literature. In other words, incorporating granular contract and time period fixed effects constitutes an unobserved heterogeneity "catch-all" approach in terms of adjusting for lateral (i.e., between contract) as well as temporal (i.e., between times) heterogeneities; whatever they may be. Activity, Size, and Connectance are natural log transformed in order to better fit exponential growth trajectories to a linear trajectory-based modeling approach. As a result, any such coefficients should be interpreted in percentage change to percentage change terms. For example, a model coefficient of 0.10 suggests that a 1 percent change in the independent variable is associated with a 0.10 percent change in the dependent variable. Because LGM places primary focus on the slope, the effect of the independent variable refers to the percentage change in activity growth. To avoid oversaturation (i.e., by using all 106 potential model periods), I increment each measurement window by three periods such that each contract can encompass 36 growth curves at most: T1 (i.e., growth curve from T1-T6) to T2 (i.e., growth curve from T4-T9), through to T106 (i.e., growth curve from T106-T112). Figure 4-4 below illustrates the LGM approach using 61 Contract 0f5d2fb29fb7d3cfee444a200298f468908cc942 (ledger for Decentraland: MANA Token) was set as the reference category due to having the maximum possible analyzable observations, as well as having the closest overall mean activity level to the dataset mean while also retaining the lowest standard deviation. 62 Time period T64, comprised of intervals ranging from weeks 190 to 195, was used as the reference category due to having the most observations of all time periods. 118 a blue curve to represent activity levels and red dotted lines to represent growth curves across seven measurement occasions: Figure 4-4: Illustration of Latent Growth Curve Modeling Approach Each period follows a six-step modeling approach; adding independent variables sequentially with each iteration. First, the baseline model predicts the latent activity level slope and intercept using only the control variables: network size, contract fixed effects, and time period fixed effects. Model 2 adds connectance. Model 3 adds centralization. Model 4 adds clustering. Model 5 adds centralized clustering. Finally, model 6 adds cross-functionality63. Before modeling, it is useful to get a high-level overview of the key variables in the final analysis dataset. Table 4-2 below provides a descriptive summary of this dissertation’s key variables. The last row details the number of contracts represented in the final analysis dataset. 63 Code used to set up and analyze data is available at: https://github.com/dennisgma/dissertation 119 Following immediately after, Table 4-3 provides pairwise correlations between all variables of interest. Table 4-2: Descriptive Statistics Variable (T1) N Mean Standard Deviation Minimum Maximum Time Period 3,400 60.893 27.891 1.000 106.000 Activity(logn) 3,400 7.849 1.780 3.912 13.899 Size(logn) 3,400 11.431 1.418 5.501 14.553 Connectance(logn) 3,400 7.145 1.764 1.609 13.748 Centralization 3,400 0.00004 0.00020 1.29E-07 0.00273 Clustering 3,400 0.116 0.156 0.000 1.000 Centralized Clustering 3,400 0.148 0.263 0.000 3.000 Cross-functionality 3,400 0.106 0.140 0.000 1.200 Contract Observations 171 19.170 11.533 1.000 36.000 Table 4-3: Correlation Matrix64 1 2 3 4 5 6 7 8 9 10 11 12 Time Period 1 1 Activity(T1) 2 -0.05 1 Activity(T2) 3 -0.04 0.80 1 Activity(T3) 4 -0.07 0.75 0.83 1 Activity(T4) 5 -0.07 0.71 0.77 0.85 1 Activity(T5) 6 -0.06 0.69 0.76 0.78 0.84 1 Activity(T6) 7 -0.09 0.65 0.71 0.76 0.78 0.83 1 Size 8 -0.15 -0.09 -0.05 -0.07 -0.06 -0.06 -0.06 1 Connectance 9 -0.11 0.84 0.68 0.62 0.59 0.57 0.53 0.27 1 Centralization10 -0.02 0.10 0.07 0.08 0.07 0.07 0.07 -0.55 -0.29 1 Clustering 11 -0.06 0.23 0.18 0.18 0.18 0.19 0.20 -0.21 0.14 0.06 1 Centr. Clustering 12 0.06 -0.14 -0.18 -0.15 -0.16 -0.16 -0.14 -0.39 -0.39 0.49 0.13 1 Cross-functionality 13 -0.16 -0.26 -0.19 -0.15 -0.13 -0.13 -0.11 0.23 -0.09 -0.12 -0.14 -0.14 64 All correlation coefficients are statistically significant at p<.05, except for Centralization x Time Period. It is noteworthy that some correlations are notably high. This is to be expected particularly for some network variables. For instance, centralized clustering is a restricted case of clustering; yet it is important to model the former in context of the later in order to pull its effects out. 120 CHAPTER 5: RESULTS The model results can be separated into two outcomes, intercept and slope, across two themes: network size and structure. The latent intercept can be construed as the initial stock of activity whereas the slope represents activity growth over time. Although all hypotheses concern the latent slope component, the latent intercept contains important information on how each independent variable relates to the immediate stock of activity; thereby providing more comprehensive analyses of platform activity dynamics. Model 1 serves as a baseline model with network size and includes comprehensive contract fixed effects as well as time period fixed effects. This baseline model is fundamentally important in that it models the impact of network size on activity, holding all contextual factors constant. The model directly examines the mental model presently pervading the platforms literature. I emphasize here that the anticipated relationship is positive exponential (β>1.00 as activity and size are both log-transformed) and that few studies empirically model the exponential growth hypothesis, despite its prevalence65. Subsequent models phase in network organization variables corresponding to each hypothesis, which focus on the relation between connectance, centralization, clustering, centralized clustering, and cross-functionality and the latent activity slope. It is important to note that activity, size, and connectance are natural log transformed due to the expected exponential relationship between the independent variables and activity growth. Transforming these variables helps to linearize the otherwise accelerating growth trajectory (Willett & Bub, 2014), in addition 65 Exceptions are studies demonstrating Metcalfe’s law with respect to network size’s exponential relationship to economic value (e.g., Alabi, 2017; Peterson, 2018). Due to its prevalence, it remains unclear if the mediating mechanism between size and economic value is driven by the widespread subscription to Metcalfe’s law itself (i.e., self-fulfilling prophecy); and how robust this relationship is across contexts (cf. Briscoe, Odlyzko, & Tilly, 2006). 121 to easing interpretation: that is, the latent slope coefficient for a given independent variable represents a percentage change in activity growth given a percentage change in the predictor. Table 5-1 presents this dissertation’s analytical results across a set of six models. The latent growth models successively phase in a network variable corresponding to each hypothesis. This chapter references Table 5-1, moving incrementally from Model 1 through to Model 6. Table 5-1: Latent Growth Model Results Model 1 Model 2 Model 3 Model 4 Model 5 Model 6Intercept Size 0.693*** 0.121*** 0.122*** 0.122*** 0.126*** 0.139*** Connectance 0.904*** 0.905*** 0.905*** 0.900*** 0.886*** Centralization -1245.6** -1246.4** -1277.4** -1318.7** Clustering 0.002 0.019 0.014 Centralized Clustering -0.118 -0.141 Cross-Functionality -0.684*** Constant NO NO NO NO NO NO Time Period FE YES YES YES YES YES YES Contract FE YES YES YES YES YES YES Slope Size -0.007 0.038*** 0.038*** 0.039*** 0.039*** 0.036*** Connectance -0.072*** -0.072*** -0.074*** -0.074*** -0.071*** Centralization 101.13 63.805 64.022 72.667 Clustering 0.103* 0.103* 0.104* Centralized Clustering 0.001 0.006 Cross-Functionality 0.143** Constant NO NO NO NO NO NO Time Period FE YES YES YES YES YES YES Contract FE YES YES YES YES YES YES Res. Var. (Activityt0-5) 0.675*** 0.629*** 0.629*** 0.629*** 0.629*** 0.628*** Res. Var. (Intercept) 1.367*** 0.230*** 0.229*** 0.229*** 0.228*** 0.225*** Res. Var. (Slope) 0.026*** 0.040*** 0.040*** 0.040*** 0.040*** 0.040*** N 3400 3400 3400 3400 3400 3400 CD .716 .951 .951 .952 .952 .952 Log Likelihood 898929 895709 926679 929144 930635 933428 SRMR .0024 .0025 .0025 .0025 .0025 .0025 *= p<.05; ** = p<.01; *** = p<.001 122 Size (Model 1) Model 1 serves as a baseline: modeling only the effect of network size, while controlling for contract and time period fixed effects. This analytical approach isolates the effects of network size above and beyond contextual factors. As a starting model, this model specification establishes an important analytical framing. Specifically, it sets up a ceteris paribus examination of how network size impacts activity levels. As expected, the model latent intercept indicates a positive relationship between network size and immediate activity levels (β=.693; p<.001). However, these same baseline model results suggest that network size has a non-significant relationship with activity growth (β=-.007; p>.05); net of contract and time period fixed effects. The Model 1 results are particularly striking because network size’s relationship with activity growth is not statistically significant. These results do not support the predominant view that larger platform networks prosper; suggesting that network effects are not inherent. Connectance (Model 2) Model 2 adds connectance. Connectance serves as baseline measure of network completeness. In addition to demonstrating a statistically significant effect on both the activity intercept (β=.904; p<.001) and slope (β=-.072; p<.001), adding connectance generates some notable shifts from the baseline model. First, the model’s latent activity intercept coefficients are both positive, suggesting that both size and connectance relate to the initial activity stock. However, connectance has a larger coefficient than size. Taken into context of their respective scales, connectance can be viewed as 123 having larger predictive power than size when it comes to activity’s latent intercept. Although the size coefficient is notably diminished (i.e., from β=.693 in Model 1 to β=.121 in Model 2), the results suggest that connectance only partially mediates the relationship between size and activity’s latent intercept. Second, network size’s latent slope coefficient becomes statistically significant with a positive slope (β=.038; p<.001). With the only difference being the addition of connectance, the results suggest that size’s impact on activity growth can better be understood after adjusting for connectance. On a theoretical level, this supports the notion that connectance cannot be inferred from size. However, the direction of the latent slope coefficients run counter to this dissertation’s expectations. Rather than fully mediated size effect in conjunction with a positive connectance coefficient, the model results suggest that size has a positive relationship with activity growth in light of partitioning from connectance’s negative relationship. While the results do suggest that connectance and size are enmeshed—the ways in which they unravel are surprising. Third, the coefficient of determination (CD) has increased from the already high 0.716 of Model 1 to Model 2’s 0.951. The CD can be interpreted in the same way as a model R-squared in linear regression. Therefore, the addition of connectance increases the percentage of variation explained by the model from 71.6% to 95.1%. At a high level, these model updates indicate that network connections play a substantive role in explaining platform activity. Keeping in mind that the models are loaded with comprehensive contextual variables in the form of time period fixed effects and contract fixed effects, Model 2’s results provide compelling evidence on the crucial role of network connections. These results suggest that while greater connectance relates to the immediate stock of activity (i.e., intercept), being connected alone does not sustain or even grow future activity (i.e., 124 slope). The opposite relation exists: present period connectance exhibits a negative activity slope. Therefore, H1 that connectance has a positive effect on activity growth is rejected. However, the general relationship between connectance and activity merits examination. It is important to highlight that although it is a network measure, connectance provides limited detail on how a network is structured. Therefore, the relationship between connectance and activity—that initial activity stocks are positively related, and growth is negatively related and at a much lower magnitude—risks being misconstrued. Because this dissertation emphasizes the role of network structure on activity growth, no hypotheses were developed around the immediate effects of network characteristics and their relation to the immediate stock of activity. However, the model results are nevertheless illuminating. Connectance, while relating to higher initial activity, appears to generate inertia. Connectance does not sustain activity; it depresses it over time. Taking connectance’s effect on activity as whole (i.e., considering intercept and slope), it is important to note that the decline is miniscule compared to the initial activity attribution. The remaining models phase in this dissertation’s network structural measures, and model their relationships with activity growth. Centralization (Model 3) Model 3 adds centralization. Centralization approximates economies of scale. The model results do not support H2 that centralization has a positive relationship with activity growth (β=101.13; p>.05). However, there is a statistically significant relationship between centralization and the latent activity intercept (β=-1245.6; p<.01). Due to centralization’s scale (Mean=0.00004), model coefficients are relatively large. No other substantive coefficient 125 changes appear in the model. Taking all statistically significant coefficients (p<.05) at their means provides the latent growth curve: ActivityM3 = -.075Time + 7.811 Clustering (Model 4) Model 4 adds clustering. Clustering approximates network cohesion, which relates to resilience. The model results support H3 that clustering has a positive relationship with activity growth (β=.103; p<.05). There is no statistically significant relationship between clustering and the latent activity intercept. No other substantive changes appear in the model. Taking all statistically significant coefficients (p<.05) at their mean provides the latent growth curve: ActivityM4 = -.071Time + 7.811 Centralized Clustering (Model 5) Model 5 adds centralized clustering. Centralized clustering approximates the degree to which dense hubs are present in the network. The model results do not support H4 that centralized clustering has a positive relationship with activity growth (β=-.004; p>.05). There is no statistically significant relationship between centralized clustering and the activity intercept. No other substantive changes appear in the model. 126 Cross-functionality (Model 6) Model 6 adds cross-functionality. Cross-functionality utilizes network motifs to detect the degree to which network components take on multiple roles. The model results support H5 that cross-functionality has a positive relationship with activity growth (β=.143; p<.01). However, a negative relationship between cross-functionality and immediate activity exists, as indicated by the activity intercept term (β=-.684; p<.001). The final results provide an initial model from which to further understanding of network activity dynamics. At a high level, the model detects four network properties that impact activity growth in various ways. Two resilience-oriented structural properties—clustering and cross-functionality—both exhibit a positive effect on activity growth. Connectance, which has a positive relationship with initial activity levels, exhibits a negative activity slope. Cross-functionality exhibits the opposite relationship with a negative effect on activity intercept and a positive activity slope effect. However, there are differences in effect magnitude between these last two more nuanced network properties. While cross-functionality’s positive slope can offset the initial lowered activity within a five-week period, connectance’s negative slope won’t equalize the initial positive activity until approaching twelve weeks (assuming the model can be extrapolated past its six-week boundary). The final model does not support any effect of centralized clustering on activity. Taking all statistically significant coefficients (p<.05) at their means provides the latent growth curve: ActivityM6 = -.068Time + 7.802 To illustrate the magnitude of the various network variables, I plot the latent growth trajectories at high (+1 standard deviation from the mean) and low (-1 standard deviation from 127 the mean) levels of the network variable across both the latent intercept and latent slope equations. Figures 5-1 to 5-5 present the latent growth curves for size, connectance, centralization, clustering, and cross-functionality, respectively. Figure 5-6 graphs latent growth curves for a combined high (+1 standard deviation from the mean for positive coefficients and -1 standard deviation from the mean for negative coefficients) and combined low (+1 standard deviation from the mean for negative coefficients and -1 standard deviation from the mean for positive coefficients). Figure 5-1: Latent Activity Growth Trajectories by Size (High vs. Low) 128 Figure 5-2: Latent Activity Growth Trajectories by Connectance (High vs. Low) Figure 5-3: Latent Activity Growth Trajectories by Centralization (High vs. Low) 129 Figure 5-4: Latent Activity Growth Trajectories by Clustering (High vs. Low) Figure 5-5: Latent Activity Growth Trajectories by Cross-Functionality (High vs. Low) 130 Figure 5-6: Latent Activity Growth Trajectories by Positive Coefficients (High vs. Low) At first glance the singular network variable based latent growth curves do not appear to vary to a large degree when comparing higher (+1 standard deviation from the mean) to lower (-1 standard deviation from the mean) levels. However, some key considerations underscore these latent growth curve changes. First, although the contribution towards activity for being above average on any one network dimension exhibits only minor deviation from the mean level—and indeed even low level—latent growth curve, Figure 5-6 highlights that when network dimensions optimize in a combined manner across several network properties66, the resulting impact on activity growth is discernable. Second, activity is natural log scaled. Although the depicted latent growth curves differ at times by merely a fraction of a unit, inversing the transformation through 66 Network measures are not totally independent of each other. I checked on the validity of the +/- 1 standard deviation curves by taking observing the range of all variables using a size-based subset at +1 standard deviation to maximum (N=452) and minimum to -1 standard deviation (N=400). For both groups, all variables had their respective mean +/- 1 standard deviation values within range, except for centralization. Centralization was barely out of range in the -1 standard deviation case, and considerably out of range in the +1 standard deviation case. 131 exponentiation reveals differences that are orders of magnitude in scale. For instance, e10 is 22026 whereas e8 is 2981; and e5 is only 148. Robustness Checks The primary analyses reveal intriguing and complex dynamics around platform activity organization. However, typical modeling questions also come to the fore: how robust are the model results? Is omitted variable bias (e.g., endogeneity, unobserved heterogeneity, etc.) a concern? In this next section, I leverage the opportunity to conduct robustness checks in these areas through additional analyses. Specifically, I repeat modeling given a lower half subsample (N=1754 across 97 contracts, by removing the highest 50% of contracts in terms of overall activity), and by including a constant term in both the latent intercept and slope equations. Table 5-2 highlights the results of these robustness checks against the completed Model 6 results from the initial analyses: 132 Table 5-2: Latent Growth Model Results (Robustness Checks) Model 6 Model 7 Model 8 Model 9 Support Intercept Size 0.139*** 1.004 0.135*** 12.22*** Connectance 0.886*** 0.885*** 0.900*** 0.873*** Centralization -1318.7** -1268.1** -3449.5 879.6 Clustering 0.014 0.015 -0.110 -0.129 Centralized Clustering -0.141 -0.137 0.005 0.038 Cross-Functionality -0.684*** -0.683*** -0.474** -0.440** Constant NO -9.788 NO -136.94*** Time Period FE YES YES YES YES Contract FE YES YES YES YES Slope Size 0.036*** 1.158 0.031*** 2.468* Connectance -0.071*** -0.073*** -0.066*** -0.072*** H1:No Centralization 72.67 138.30 1559.1 2431.8* H2:No Clustering 0.104* 0.106** 0.109* 0.106 H3:Yes Centralized Clustering 0.006 0.011 0.024 0.031 H4:No Cross-Functionality 0.143** 0.144** 0.131* 0.137* H5:Yes Constant NO -12.705 NO -27.60* Time Period FE YES YES YES YES Contract FE YES YES YES YES Res. Var. (Activityt0-5) 0.628*** 0.628*** 0.619*** 0.619*** Res. Var. (Intercept) 0.225*** 0.225*** 0.199*** 0.191*** Res. Var. (Slope) 0.040*** 0.040*** 0.033*** 0.032*** N 3400 3400 1754 1754 CD .952 .952 .948 .950 Log Likelihood 933428 933430 219200 219223 SRMR .0025 .0025 0.0054 0.0054 *= p<.05; ** = p<.01; *** = p<.001 Full sample with constant terms (Model 7) Constant terms are available for both latent intercept and latent slope equations. Model 7 adds constant terms to both the latent intercept and latent slope equations. Constant terms represent the mean activity intercept and mean activity slope when all other variables are at 0. When network aspects are at 0, initial activity and activity growth should also be 0. Therefore, the theoretical justification for including constant terms is lacking. Hence, their absence in the 133 primary analyses. However, the option to include constant terms in latent growth curve models offers the potential to perform sensitivity analysis on the model’s independent variables. Given the comprehensive set of predictors, which include contract and time period fixed effects, toggling constant terms reveals which predictors are sensitive to a fixed adjustment to the right-hand side of each latent variable equation. While constant terms are not variables themselves (omitted variable biases technically pertain to variables, whereas constants are fixed), they do adjust the relationship between the predictors and estimated latent variables while absorbing bias. The way in which the constant adjusts these relationships vary according to the extent that predictors are biased or sensitive to omitted variables (e.g., due to being correlated with model error; endogeneity). Leveraging this opportunity is especially valuable to the present analytical context—where the proposed latent growth curve represents a “fully specified” model. Taking all statistically significant coefficients (p<.05) at their means provides the latent growth model: ActivityM7 = -.494Time + 6.202 Given that Model 6 already represents an “everything but the kitchen sink” approach with the comprehensive set of network variables and fixed effects for contract and time period, the constant terms essentially act as the “kitchen sink.” Even though the constant terms themselves are not statistically significant, it is informative to examine changes to the remaining model coefficients. Most notable is the loss in statistical significance from network size in both equations. Even though neither constant term is statistically significant, the results are telling: a previously unobserved factor intervenes on the relationship between network size and activity in such a way that size is no longer directly predictive of activity’s latent intercept or latent slope. Taken alone, the results suggest that network size does not directly impact activity. However, the actual 134 relationship may be more complex. I elaborate on this point through the remainder of this chapter (i.e., contrasting the results using a lower 50% subsample), and discuss a potential resolution further in Chapter 6: Discussion and Conclusion (i.e., incorporating competitive crowding in future analysis). These “fully specified” model results can be further evaluated against a set of reduced sample robustness checks to investigate the possibility of outlier-driven results. The following models replicate Model 6 and Model 7 using a lower 50% subsample (i.e., removing 100 of the highest activity contracts overall)67. Lower 50% subsample without constant terms (Model 8) Model 8 is a lower 50% subsample of Model 6; intended as a robustness check against outlier-driven results. The only notable model change between Model 8 and Model 6 is around centralization. In Model 8, the latent intercept coefficient is not statistically significant. These model differences are accounted for only by the removal of the top 50% of the sample in terms of overall activity. Altogether, the model differences suggest that the higher activity contracts have a more cohesive relationship between network centralization and initial activity stocks. Taking all statistically significant coefficients (p<.05) at their means provides the latent growth curve: ActivityM8 = -.080Time + 7.574 67 Conducting a robustness check by removing the top and bottom “edges” of the full sample is common practice. However, this dissertation uses a sample of the 200 most active Ethereum Metropolis contracts. Therefore, I opt to subsample the bottom half of the most active contracts; as removing from the lower range of contracts would be meaningless, since the full analysis sample already represents the top-most tail of all Ethereum contracts. I discuss these implications further at the end of this chapter. 135 Altogether, the differences between Model 6 and Model 8 are not substantive. As such, it is not particularly surprising that the overall latent growth curve models are essentially the same. Taken as an isolated comparison, the Model 8 results strongly support the robustness of Model 6. Lower 50% subsample with constant terms (Model 9) In the next model, a constant term is added to both the latent intercept as well as the latent slope equations. Model 9 essentially acts as a robustness check to Model 8 as well as Model 7. Taking all statistically significant coefficients (p<.05) at their means provides the latent growth curve: ActivityM9 = -.616Time + 4.665 In comparison to both Model 6 and Model 8, adding constant terms adjusts two key variables in general: size (both robustness checks) and centralization (lower 50% subsample only). Evaluating across various robustness checks helps to organize an overall assessment. First, comparing Model 8 and Model 9 reveals that adding a constant term to both the latent intercept and latent slope equations adjusts the relationship with network size in both equations. Although size is statistically significant in both sets of half-sample models (i.e., Models 8 and 9), the magnitude of the coefficients after including a constant term in both the latent intercept and the latent slope equations are significantly higher. One particularly noteworthy coefficient is the network size latent slope coefficient (β=2.468; p<.05). With a coefficient well over 1.000, these results demonstrate support for the size hypothesis—that platform networks grow exponentially as a function of size. However, it remains possible that these results are driven by range restriction; or perhaps something else. 136 Second, contrasting changes in models due to the addition of constant terms across model sets (i.e., comparing Models 6 and 7 to Models 8 and 9) also reveals stark differences. The effect of adding constants to Model 6 versus Model 8 are completely different: in the full sample (i.e., Models 6 and 7), size loses statistical significance whereas in the lower 50% subsample (i.e., Models 8 and 9), size immensely increases in magnitude. In the latter model, the constants are statistically significant and of large magnitude as well. While the constant term adjustments both impact the same variable across models, the variable is impacted in opposite directions. The singular element driving the difference in results is the exclusion of observations from the highest activity contracts. The full data better fits a latent growth model where neither size nor constant coefficients are statistically significant, whereas the bottom 50% data better fits a latent growth model where both size and constant coefficients are statistically significant—and of high magnitude. It is worthwhile to emphasize at this point that the highest activity contracts have a broad range of activity levels throughout time periods (i.e., they are not high throughout all time periods, and the present analytical approach leverages variance throughout time periods). The notable area where the top half of contracts differ from the sample’s bottom half are in maximum activity levels. Therefore, the set of higher activity contracts’ relationship between size and activity is either far less cohesive or significantly lower than that of the lower activity contracts; or both. Put simply, the higher activity contracts do not maintain the same size-activity relationship after adjusting for constant terms. Why would the omission of the most active contracts tighten and magnify the relationship between size and activity so drastically (in the constant-included models)? Perhaps the question is more aptly framed as: why does including the most active contracts eliminate the relationship between size and activity (in the constant-included models)? What factor is the constant 137 encapsulating that would adjust the size-activity direction in one way without the most active platforms, but the other way (i.e., negated) when the most active platforms are included—and especially after all possible factors have been controlled for? One very plausible answer comes from work foundational to this dissertation. In their study of the video game console industry, Shankar and Bayus (2003) found that large adjacent competitors enacting a get-big-quick strategy did so at their own detriment; generating opportunities for differentiated platforms with smaller but stronger networks. While the present analyses utilize an exhaustive set of variables, even explaining 95% of total variance, platforms’ competitive crowding remains unaccounted for in the present analyses. If Shankar and Bayus (2003) generalizes to broader platform contexts, the degree to which platforms are subject to competitive pressures (e.g., via adjacent platforms) could very likely contextualize the size-activity relationship. Such a factor may well explain the patterns apparent in the robustness check models as contracts at the top end may disproportionately represent platforms in competitively saturated spaces. Removing such platforms would explain the stark difference between the Model 6 to 7 change versus the Model 8 to 9 change (i.e., when adding constant terms). I discuss avenues for incorporating competitive crowding as well as propositions for opportunities for future empirical research in Chapter 6 and Appendix A. The shift in network centralization’s significance may well be attributable to the same contextual factors. That is, centralization’s relationship with activity growth is plausibly contingent upon platforms’ competitive environment, which would explain why centralization is statistically significant in the fully adjusted (constant included) robustness check model (highest activity platforms removed), but not in preceding models. This dissertation’s particularly conservative empirical approach to incorporating centralization may also be at least partly 138 responsible for the centralization’s mixed results. Specifically, centralization is measured at an initial time period (i.e., T1). I do not measure a platform’s capacity to maintain a given level of centralization. This is a potentially important consideration as increasingly centralized networks are inherently also increasingly fragile. When highly centralized nodes are removed and their connections compromised, the overall network’s performance should suffer68. Taken into context, it is entirely possible that competitive pressures are disproportionately represented at the top end of the contract sample. As such, one possibility would be that centralization disproportionately encompasses fragility at the sample top end. If true, future studies should take explicit care to separate centralization’s fragility aspects from its efficiency aspects. As well, clustering is no longer statistically significant (β=.106; p=.052). However, the increase in the variable’s p-value is nominal. With the model results based on a substantially decreased sample drawn from 97 contracts, it is entirely plausible that the shift in statistical significance be attributed to diminished statistical power. As such, I maintain that H3—that clustering has a positive relationship with activity growth—still gathers overall support from this dissertation’s analyses. These results provide general support for H3 and H5. Although a comprehensive modeling approach was taken using contract and time-period fixed effects, along with two intersecting robustness checks, the results suggest that additional analyses are well motivated. 68 One relatively recent example in the digital platform context is Joe Rogan and Spotify (e.g., Jones & Morris, 2022), the world’s most popular music streaming platform. Joe Rogan’s podcast is Spotify’s most popular broadcast. At the beginning of 2022, Rogan was accused of espousing Covid-19 misinformation on his podcast; garnering protests and boycotts from high-profile artists including Neil Young. Due to the podcast’s prevalence, the controversy received widespread attention. A consumer poll found that 19% of the platform’s customers cancelled, or planned to cancel, their subscription following the incident (Spangler, 2022). Moreover, Spotify lost over $2b in market capitalization in the three days that followed Neil Young pulling his music over Joe Rogan’s podcast statements (Lawrence 2022). Although this particular example doesn’t illustrate the loss of a highly central network component, it does illustrate the weight that such a central component can carry—and its commensurate impact on the platform network in general. 139 Network dynamics are complex across systems contexts. Platforms are no different. The results suggest that additional research should be conducted in order to understand the complex mechanisms at play. However, much like the network science literature demonstrates, there are also general relationships. Overall, the results paint a portrait not necessarily of growth; but rather of resilience and resistance to decline. The positive effects of the resilience-oriented measures—clustering and cross-functionality—substantiate the resilience-driven hypotheses outlined in this dissertation. Nevertheless, the more complex trade-off relationship between cross-functionality and activity (i.e., with positive growth at the cost of lowered immediate activity) merits further examination. I discuss these items, and more, in the next chapter. 140 CHAPTER 6: DISCUSSION AND CONCLUSION Platforms increasingly organize social and economic activity. Until now, platforms scholarship has largely overlooked how this increasingly ubiquitous organizational form actually organizes activity. Although mounting research underscores platforms’ network structural properties as a key determinant of platform outcomes, a cohesive paradigm addressing this crucial topic remains remarkably absent. By mobilizing central concepts from the rich and already well-developed network paradigm, this dissertation develops and empirically tests several structurally focused hypotheses around platform network activity dynamics using novel Ethereum blockchain data. The overall results support this dissertation’s general proposition that network organization impacts platform activity development. The ways in which platforms organize activity directly influences subsequent activity growth—and decline. In the following sections, I conclude by highlighting this dissertation’s contributions, limitations, future directions, and implications. Theoretical Contributions This dissertation formalizes a network organizational view of the platform and makes four key contributions to platforms research by: (1) positioning platform activity as the core research tenet, (2) formalizing a network organizational approach, (3) isolating the effects of network structure from size, and (4) demonstrating blockchain data as a promising empirical opportunity. 141 Activity as primary analytical unit First, this dissertation introduces platform activity as the primary analytical unit. Platform-mediated activity is the most granular analytical unit, both theoretically and empirically. Centering analysis around platform activity serves to broaden and add flexibility to the general platforms research agenda for three key reasons owing to activity’s generativity, generality, and consequentiality. As demonstrated in the present dissertation, platform activity is highly generative due to its multitude of potential properties. When elaborated as interactions or transactions, activity can facilitate the construction of higher-level structures (i.e., activity networks). Platform activity resolves a critical bottleneck constricting current platforms research by acting as the building block for defining network structure. Though not explored in this dissertation, activity can also elaborate typological, value/valence, temporal, and geospatial properties—which can be leveraged theoretically and empirically69. Activity is general in that all platforms ultimately provide a means towards achieving a particular activity of purported value (e.g., selling/buying goods/services). That is, all platforms can be discussed in terms of some core mediated activity of value. Such a high degree of abstraction suggests that theory based on platform activity has the potential to be highly generalized. I elaborate on examples in the future directions section at the end of this chapter. On that same vein, no outcome is more consequential than platform activity. The current literature focuses on platforms’ network size—but to what end? Platforms ultimately develop networks mediating valuable activity. Moreover, contemporary platform environments provide 69 I discuss this particular aspect in greater detail in the future directions section. 142 frictionless (i.e., costless) membership; and as a result, network size becomes less reliable as a proxy for activity and platform value. Formalizing platform network theory Second, formalizing a network-based perspective delivers a clear solution to the mounting concerns around theoretically black-boxing platform networks. The platforms literature increasingly highlights the centrality of network dynamics, signaling the need for a coherent approach to network analysis. This dissertation introduces foundational network concepts and develops hypotheses commensurate to their theoretical implications on platform systems. Empirically testing these hypotheses while holding macro-structural factors constant (i.e., via comprehensively modeling fixed effects) and controlling for network size is a rigorous approach to isolate network-structural effects. Distinguishing the role of network structure beyond size is a cornerstone issue facing present platforms literature. As well, this dissertation directly answers a long-heeded call from the administrative sciences for a network theory of organization (Salancik, 1995). My findings suggest that, indeed, “network structure reflects much about the functioning of organizations and, possibly, their coordination failures or achievements” (Salancik, 1995, p. 346). This dissertation essentially opens an interface for importing the network paradigm to platform contexts by providing a generalized definition of platforms and a basis for constructing networks via platform activity. In doing so, the vast, richly developed, network science toolkit can be explored and adapted for platform analysis by means of their activity structures. This 143 dissertation’s results are clear: network structure matters. By leveraging decades of network science, platforms research can finally begin to elaborate how. Structure, not just size Third, this dissertation validates a key argument bottlenecking platforms research: that network structure plays a central role in platform dynamics, independent from network size. Mounting research increasingly suggests that network quality and structure plays a critical role in platform dynamics. However, stringent empirical evidence has since been lacking. This dissertation makes a significant step into the foray of exploring platform level dynamics from a network organizational lens by directly engaging the structure versus size debate. The impact of structure cannot be taken for granted; nor can it be inferred from network size. This advancement is decisively important for a confluence of reasons. This dissertation’s analysis challenges the approach guiding contemporary strategic management theory on platform dynamics, which relies on the inherency of network size-centered exponential scaling dynamics driven by taken-for-granted network effects. The results, which utilize a rigorous approach to isolate structural effects from network size, show no evidence of such inherency. Network size’s relationship with platform activity is more nuanced than we currently understand. When taken into context, platform networks are not self-expanding structures that grow exponentially. Nor do they necessarily grow recursively. When it comes to network size, platforms are idiosyncratic. However, when it comes to network structure, there exist general 144 relationships between the ways in which platforms organize activity and their subsequent growth—or resistance to decline. The results build a new direction for past work which rely on assumptions around recursive growth dynamics, and winner-take-all views to platform competition. The volume of platforms research centered around network size is substantial, as size has been so foundational—both as the “be-all” and “end-all.” More specifically, research has utilized network size as the primary outcome of interest as well as the proxy for the principle mechanism (i.e., network effects). This dissertation challenges size’s relevance in both domains. Most contemporary (i.e., digital) platforms encompass minimal adoption or membership costs: it would be more theoretically accurate and conservative to assume that all components are inherently available to all platforms (i.e., fully multi-homed; as in websites to search engine platforms) than it is to presume that a component is locked into a singular platform (e.g., in the case of a high investment deeply embedded standard such as the QWERTY keyboard). As such, size loses ecological and theoretical significance as an outcome. With size demonstrated as an unreliable proxy for network effects, the mechanisms guiding platform dynamics can no longer be taken for granted. Rather, identifying and elaborating on these mechanisms and their potential contingencies should be of central focus. To clarify, this dissertation does not prescribe the wholesale abandonment of network size: just an elaboration of its theoretical boundaries and ecological scope. Just as much of the technology management’s literature around platforms is imprinted in contexts with high membership and adoption costs (and, therefore, switching costs), it remains likely that such contextual domains can very well validate network size’s ability to predict network competitive 145 outcomes. As such, more work needs to be done to define network size’s practical boundaries; particularly as it is among the most accessible platform metrics available across contexts70. Blockchain data: A promising empirical opportunity Fourth, this dissertation’s empirical context is one of very few studies to analyze complete network data in a temporally dynamic way. Though empirical contributions can oftentimes be discounted in fields facing theoretical bottlenecks, the opposite case exists in the broader network sciences in that complete multi-network studies—temporal dynamics notwithstanding—are treasured. Complete network data is rare, and this dissertation introduces blockchain data as a trove of opportunity for network analysis. Scholars are increasingly recognizing the generative potential of blockchain technology to organizations and institutions (Allen et al., 2020). If blockchains or other distributed trust- 70 It is worthwhile here to revisit the contrast between platforms and traditional organizations alluded to in this dissertation’s introduction. The analysis results highlight parallels to the classic corporate literature from organizational theory, particularly around size and centralization. For instance, classic research on formal organizations elicits a similar elaboration on the nuances and significance of organizational size (e.g., Kimberly, 1976). Foundational theory suggests strategically beneficial effects with size (e.g., Freeman, Carroll & Hannan, 1983) and centralization (e.g., Pfeffer & Salancik, 1978), paralleling the model results in the final robustness condition. The theory further suggests that market power can attenuate external political pressures (e.g., Haveman, 1993; Pfeffer & Salancik, 1978)—an image that clearly parallels current large platform-based technology firms. However, there are key definitional distinctions that serve to substantially differentiate platforms from hierarchies. These differences revolve around the very mechanisms that formulate the ways that the distinct forms organize activity. Platforms rely on technical authentication, which is reductive and definitive. Formal hierarchies, on the other hand, rely on legal authority, which can be imperfect (though purportedly rational). These imperfections can formulate a basis for individual and group discretion which can generally aggregate upwards as internal politics. Political inertia can be particularly present and detrimental for larger organizations with respect to their capacity to adapt (e.g., Haveman, 1993) and ultimately survive (Hannan & Freeman, 1984). Regardless, comparing platform network centralization and size to the centralization and size of traditional organizations, though thought-provoking, is ultimately an incompatible juxtaposition. After all, at the helm of each platform is typically such a traditional organization. Therefore, perhaps a more apples-to-apples comparison, which clearly demonstrates how platforms differ, is to compare their administrative hierarchies to those of traditional organizations. Where traditional organizations scale their organization in tandem with the scale of their operations to maintain span of control, platform administrative organizations scale operations without requiring internal scaling (i.e., the internal organization size does not change much). As a result, platforms can forego certain size-based liabilities (e.g., internal politics) while incurring size-based benefits (e.g., market power). 146 based ledgers pervade contexts such as specific industries, empirical opportunities to study those contexts under a network dynamic lens may also become available in the future. This dissertation provides a base from which to draw for analysts interested in conducting network activity analysis based on transaction level data. Limitations This dissertation has notable limitations. However, many of them can be overcome in future studies. I identify and unpack some of these limitations, while offering recommendations for future studies. By identifying and limiting analysis to only the highest activity volume contracts, measurement on the dependent variable can be a concern. However, the concern is a minor concession when procuring complete network data, particularly with respect to the demanding dynamic analytical approach utilized in this dissertation. Indeed, all sizable networks suffer from this critique to some extent. Without a sufficiently large network, certain structural measurements cannot be taken. An even larger network is required to take repeated measurements. The empirical opportunity granted by Ethereum blockchain data, though representing a diversity of platforms, can still be construed as being relatively bounded along a variety of dimensions. Therefore, the boundaries of this dissertation’s analysis are also limited. Compared to more established platforms, Ethereum based platforms are considerably smaller both in terms of membership and activity. Future research should aim to incorporate and test the present theory under different contexts in order to clarify theoretical boundaries and validity. 147 Ethereum-specific technical concerns also exist. Take timestamps for example. It is worthwhile to note that a timestamp corresponds to a transaction’s validation time on the Ethereum blockchain. Transactions are validated in blocks consisting of multiple transactions (hence “blockchain”). Transactions are queued for validation according to the specified transaction cost accompanying them. These transaction costs are known as “gas fees.” Discrepancies exist between a transaction’s submission time and its actual validation time, depending on the demand for validation and a transaction’s allocated gas; with higher gas allotments corresponding to earlier validation. This cursory understanding of gas fees is sufficient for the scope of this dissertation. However, further detail is available in the public domain and through more technical documentation (e.g., Wood, 2014). Therefore, it is possible for a transaction submitted during one analytical time period to be validated in the next. This consideration can be nontrivial as non-random between-contract and within-contract validation inequalities can manifest. However, this dissertation’s modeling approach corrects for these potential concerns in a multitude of ways. Incorporating fixed effects addresses between-contract concerns. Where utilizing delayed transactions (i.e., shifted to the next time period) already lends itself to a more conservative empirical test, utilizing LGM to model activity growth serves to further “smooth out” noise—random or otherwise—in the predicted outcome, across multiple time periods. In addition, Ethereum and its participants are generally viewed as being more fringe compared to mainstream platforms and their participants. Blockchain systems are still considered as an emerging technology, with Ethereum’s viability for platform applications remaining limited and somewhat niche. Despite the purported variety of platform applications that utilize Ethereum, the overall participant base forming the broader Ethereum network likely differs 148 substantively from that of more established platform networks. It is plausible that micro level activity patterns may vary based on different types of platform participants. Future research can explore and incorporate the impact of heterogeneous platform participants into theory. While this dissertation's more nuanced results can benefit from elaboration in future studies, I expect the general results behind the resilience-oriented findings, particularly around clustering, to be generalizable to other contexts for at least a couple of reasons. First, as a form of distributed trust technology (Seidel, 2018), Ethereum likely supports platforms which are disproportionately transactive. These conservative contexts are less likely to elicit clustering based effects than, say, community-oriented platforms (e.g., with less transitive forms of interactions). Second, this dissertation's modeling approach is conservative (e.g., relying on six time periods to measure latent growth, controlling for comprehensive fixed effects, clustering adjusts for a multitude of other network topological measures, etc). Further research will be required to clarify the generalizability of this dissertation’s empirical findings. In opting for accessibility, this dissertation overlooks some of the more contemporary and robust measurement alternatives identified in network science. For instance, there is a plethora of approaches to centralization; each of which emphasizes slight yet meaningful variations on how networks are centralized. Future platforms research focusing on centralization can identify and elaborate which forms are best suited for capturing network centralization, and which contexts—if at all—merit toggling between different approaches to centralization. This dissertation’s treatment of centralized clustering falls short of established normalization prescriptions. For this reason, it is plausible that this particular structural concept remains inadequately measured in this dissertation. Specifically, an adjustment factor was omitted due to computational constraints. Future opportunities to detect centralized clustering 149 can follow Colizza et al. (2006). Colizza et al.’s (2006) method for rich-club detection further highlights the inherent structural tendency for large networks to develop centralized clustering (i.e., form rich clubs), even when randomly connected. Therefore, in order to appropriately account for network scale based centralized clustering tendencies, 𝛷(𝑘) should be normalized against the null network 𝛷௥௔௡ௗ௢௠(𝑘). 𝛷௥௔௡ௗ௢௠(𝑘) is the rich club coefficient of a random network with identical degree distribution to the network under study. Dividing 𝛷(𝑘) by 𝛷௥௔௡ௗ௢௠(𝑘) produces the ratio 𝜌௡௢௥௠௔௟௜௭௘ௗ(𝑘) which measures centralized clustering prevalence; discriminant from network size inherent centralized clustering tendencies (Colizza et al., 2006, p. 5): 𝜌௡௢௥௠௔௟௜௭௘ௗ(𝑘) =𝛷(𝑘)𝛷௥௔௡ௗ௢௠(𝑘) Therefore, to code the centralized clustering prevalence ratio, the analyst must first determine the minimum degree cutoff, k, to determine the subnetwork eligible for inclusion. A simple approach is to assign k as the distribution mean. Because the degree distribution of most—if not all—networks will likely be highly right skewed, thereby placing the mean well within the distribution’s tail, defining the degree cutoff in this manner would be adequate and accessible. A robustness check should then be conducted by defining k as one standard deviation above the mean distribution; thereby incorporating only the highest centrality addresses (i.e., platform components)71. Upon defining k, 𝛷(𝑘) can be calculated simply as the number of unique (and in 71 Hub identification is an important area that can be explored in future research. This particular aspect is not just important to platforms research, but network science in general. Advancements in hub detection are primarily led by disciplines such as neuroscience (e.g., Cole et al., 2010) and genomics (e.g., Alawieh et al., 2015), but it remains unclear whether approaches used in those fields can be appropriately transferred to a platforms context—and whether they might confound centralized clustering measures. Therefore, and consistent with this dissertation’s goals, I recommend a more general and accessible approach by identifying the subnetwork of hubs using a degree distribution cutoff, k. 150 this case, undirected) transactions divided by the maximum unique transactions for the subnetwork of addresses (i.e., components) with at least k unique transactions. The next step is to construct a corresponding random network with degree distribution identical to the focal network. The random network will retain the exact degree distribution as the network under study, but have its connections wired randomly. 𝛷௥௔௡ௗ௢௠(𝑘) can then be calculated and used as the divisor to 𝛷(𝑘) to obtain the normalized centralized clustering measure 𝜌௡௢௥௠௔௟௜௭௘ௗ(𝑘). Future studies will hopefully be able to make use of greater computational resources in order to incorporate a normalized version of the centralized clustering measure. It is also plausible that, in time, an efficient and prewritten library for normalized rich club (i.e., centralized clustering) detection may arise. Finally, addressing what is perhaps this dissertation’s most pressing limitation could shed light on this dissertation’s non-supported hypotheses. That is: platforms’ own environmental context. The model results suggest that unobserved confounds exist. With platform and temporal explanators exhausted, external environmental context remains the missing link. Data on environmental factors would therefore be a priority for addressing questions around non-supported hypotheses. I elaborate on avenues for incorporating environment in the proceeding section, and detail how to measure competitive context—a crucial environmental factor (e.g., Cennamo & Santalo, 2013)—in Appendix A. Despite some of the limitations inherent in this dissertation, I believe that its contributions can still make a substantial impact on platforms research. Moreover, the first steps laid out in this dissertation may well hold the generative potential to motivate subsequent network-oriented platforms research that can develop in a multitude of complimentary ways. In 151 the next section, I illustrate some recommendations for future research following from this dissertation. Future Research The most promising aspect of this dissertation is not in the questions it answers, but rather in the frontier of inquiry that it unveils. Future research arising from this dissertation can be categorized in multiple areas. I elaborate on three such themes. Extending contemporary network theory This dissertation demonstrates that the ways in which platform activity are organized significantly impacts platform activity growth. To characterize platforms' activity structures, I drew on a set of introductory concepts from the well-established network paradigm. The concepts and corresponding measures represent an accessible but nonetheless shallow introduction to how network theory can be extended to platforms contexts. Therefore, the natural next step would be to elaborate the ways in which we conceptualize platform activity organization by delving even deeper into the network paradigm toolkit. Leveraging existing network theory can develop platforms research in a multitude of ways. I consider a few such examples in following paragraphs. Future research can identify the set of concepts that most effectively and efficiently encapsulates network characteristics. There is no reason to believe that the five “Cs” identified in this dissertation’s analysis represent the most efficient set of network properties. Perhaps there is a more optimal “big five” of network properties waiting to be discovered, say, through 152 principal components analysis. Perhaps, certain structural properties can even be economized. For example, Bonacich’s approach to centralization incorporates neighbouring nodes’ centrality, thereby adjusting for centralized clustering to some extent. Perhaps network integration can be specified as a singular latent variable, or even as duo of latent efficiency and latent resilience variables. Perhaps there are constellations of prototypical integration profiles, each with distinct environmental considerations. Even within individual network structural properties such as centralization, there exist a multitude of variations—some of which may be more reliable conceptualizations in general. Perhaps it may be the case that certain variations hold different implications when taken in context. The network science literature on centralization alone is incredibly rich, and ready to be adapted to the platform context. To varying extents, the same is true of many other network properties, such as clustering. Moreover, this dissertation has only provided a shallow demonstration of what is possible with network motifs: what other network properties can be constructed or detected using these microstructural components? As well, exploring network concepts that may have been overlooked by this dissertation can hold promise. Future analyses can incorporate additional dimensions of richness by leveraging more detailed component and connection properties. For example, connections can be weighted as well as directional. This dissertation weighs all connections equally and removes directionality from the majority of network organizational concepts (with motifs being the exception). Nodes are also unweighted. However, well-developed applications are available to accommodate higher resolution analyses (Horvath, 2011) This dissertation—which focuses on introducing basic network concepts—merely scratches the surface with respect to importing network structural ideas. Decades of yet-to-be-153 integrated advancements in networks research reside in adjacent scientific disciplines such as biology, mathematics, and neuroscience. The groundwork laid out in this dissertation provides only an elementary baseline of topological concepts. Development in this stream of research would answer long-heeded calls for network level organizations research (Salancik, 1995). Perhaps, with sufficient progress, network-focused advancements in platforms research could even bolster the social sciences as a more prominent contributor to contemporary network science. Integrating platforms research Second, this dissertation opens a vast frontier of inquiry—one that provides an interface for integration with existing theory and lines of questioning. In addition to offering a direct avenue for network level analysis, this dissertation’s claim that network dynamics reside at the centre of platform organization can be systemically examined. This proposed network dynamic approach integrates naturally onto the existing literature, providing a network organizational nexus for linking platform levers to outcomes. While research on platform levers blossoms, their downstream network-level mechanisms remain obscured. With a formalized lexicon for network analysis, the effects of platform levers on outcomes including (but not limited to) activity growth can be explored through various network level mechanisms. For example, certain levers may impact activity through centralization, while others may do so through clustering. Under which circumstances do connections between upstream levers and downstream network properties strengthen, or decouple? Future research can elaborate how upstream levers relate to network properties to impact key outcomes such as activity. 154 More recently, strategic management has also zoomed in to the “value creation versus value appropriation dilemma” as a key concern. This problematization extends the zero-sum competitive framing within the platform. More recent research reveals that this particular relationship is far more nuanced (Cenamor & Frishammar, 2021). Questions around which network (sub)structures are resilient to value capture, and which are ideal to maximize capture, can be explored using network analysis. As well, network analysis can be used to test the assumption that value capture puts pressure on a platform network in a more detailed manner. Activity isn’t meant to replace network size as platform research’s key outcome. Quite the opposite: the dynamics between network growth and activity organization may hold an important key for more comprehensively understanding broader platform outcomes. Activity dynamics could perhaps act as a lynchpin for other platform outcomes, such as revenue (e.g., Cenamor & Frishammar, 2021) and innovation (see Nambisan et al., 2019). This dissertation’s approach can also be utilized to test the ecological boundaries of platform network analysis. Digital platforms are obvious: how about other contexts that fit the theoretical definition proposed in this dissertation? Can the same approach to study things such as entire economies (as platforms) on the basis of financial transactions (as interactions)? Other, less obvious, “platforms” such as public libraries or museums, could perhaps benefit from the platform network management groundwork introduced in this dissertation. Integrating with existing theory Third, this dissertation lays a springboard for additional theory development and synthesis. Structural theories abound in the organizational sciences. Exchanging between 155 existing theory and the present network dynamic platform approach can add detail to platforms research and possibly even advance more established theoretical threads. Including external dynamics to the present network dynamic approach could well unveil important contingencies to further understand platform network behaviour (Carrasco-Farré et al., 2022). For instance, niche theory can be adapted to further incorporate external dynamics such as platforms’ competitive environment. Niche crowding (Podolny et al., 1996) and positioning, or alternatives such as optimal distinctiveness (Barlow et al., 2019), can be operationalized with contemporary machine learning approaches based on platform descriptions. In Chapter 4, I allude to competitive crowding as the potential missing link in the analyses; and the potential explanator behind the robustness check model results. Though not used in this dissertation, I describe a comprehensive approach to operationalizing this potentially promising construct for future platform research in Appendix A. Volumetric approaches for characterizing a network can also be used to generate a spatial representation of platform networks. Networks of activity that are made possible by multiple intersecting platforms could be examined after integrating classic theories such as resource dependence theory. Asymmetry in (sub)networks can also be explored to provide further detail on the power dynamics occurring within platform environments based on the configuration of their respective activity networks. Offering a contemporary empirical context such as digital platforms can also plausibly extend and enrich more established theoretical perspectives, such as in this case. 156 Incorporating environment While this dissertation’s analysis utilizes comprehensive controls to capture platform level effects (e.g., via contract fixed effects) as well as general periodic effects (e.g., via time period fixed effects), the combined results suggest that contextual nuances remain to be elaborated. Therefore, although I emphasize platforms as environments, it is important to acknowledge that platforms are also subject to a multitude of contextual factors. In addition to the external competitor considerations discussed earlier, platforms can face complex pressures from a multitude of powerful external actors such as regulators (e.g., governments and legal agencies) and capital market actors (e.g., analysts and shareholders; stakeholders more broadly). These powerful external actors can have profound impacts on platforms. They can restrict the decisions available to platform administrators and they can shape the ways that platforms organize activity. In this regard, platforms are not entirely different to traditional modes of business. However, key differences remain: platforms employ a market based logic of value creation, and are simply newer. From a regulatory standpoint, this carries important implications—and follows a familiar story. Throughout the end of the 19th century, antitrust laws emerged throughout major industrial societies (Amato, 1997). The need to regulate competition continually evolved, introducing new laws along the way. The regulatory story for platforms is only just beginning to unfold. While platforms have come to rapidly scale and dominate markets in very short spans of time due to advancements in information technology and rapid adoption, regulators have not realized any such parallel to keep pace with identifying and taking regulatory action. Moreover, regulating digital platforms using traditional antitrust conventions can be mismatched and met with resistance. As a result, effective legislation may well require an 157 updated regulatory framework better suited to platforms and their distinct characteristics (Parker et al., 2020). While antitrust concerns have been fervent for years, efforts to regulate market-dominating platforms have largely reached an impasse due to a multitude of interrelated factors which differentiate platforms from traditional organizations. For example, proposals to “break up big tech” on the rationale of excessive market power are countered by arguments around network effects and economic welfare. That is, breaking up platform networks would break up network effects; and breaking up network effects would erode economic welfare (e.g., Crandall, 2019). Unlike traditional organizations, “consumers become natural allies of platforms, similarly hostile to regulations that threaten to deprive them of newfound freedoms and conveniences. In short, today’s platforms often exercise power not against the public but in a close and symbiotic alliance with a public that loves and depends on them” (Rahman & Thelen, 2019, p. 186). Though such macro-regulatory regimes are likely slower to transition, localized regulatory contexts also play a key role. For example, studies on accommodation sharing platforms such as AirBNB find that local regulation can impact platform economies in myriad nuanced ways. For example, Carrasco-Farré, Snihur, Berrone and Ricart (2022) argue that regulation can even have a legitimizing effect that can improve the survivability of platforms. Studies such as Uzunca and Borlenghi (2019) highlight the complexities inherent in platform inventory (i.e., component supply) and regulatory strictness. Even more proximal are the multitude of direct stakeholders that impact platform decisions and priorities. For instance, shareholders can pressure platform administrators to prioritize scaling and value creation versus value capture. The structure of the platform’s administrating organization(s) and its influences on network activity structure could also be an overlooked research direction. Such considerations will have consequences that unfold directly 158 in platforms’ emergent activity topology. For example: do more centralized administrators also promote centralization in activity organization? Taking these multi-layered multi-dimensional environmental contexts into account, and linking them to this dissertation’s network organizational framework, should be a priority for future platforms research. It remains crucial to understand the complex linkages between macroenvironmental dynamics and how they ultimately contextualize platforms and their emergent activity. Practical Contributions and Implications This dissertation’s findings have direct and readily applicable managerial implications. Contemporary platform management focuses on two areas: network size and platform value. These two aspects are oftentimes conflated, particularly throughout the popular discourse. As a result, platform strategy has defaulted to a “get big, fast” prescription. Platform administrators subscribing to this view risk doing so at potentially serious detriment. The practical implications stemming from this dissertation are considerable. For decades, strategic platform management prescribed aggressive network membership growth as the de facto strategy for cornering a market. This prescription remains intact to this day. Platforms continue to direct substantial financial resources to onboard new users with generous—oftentimes free and highly subsidized—initial trials. In some contexts, a substantive share of such costs are absorbed by other participants, which may lead to detrimental long-term impacts between small businesses or individuals and platforms as a category (e.g., Lei, 2021); and perhaps leading to broader societal issues as well. Indeed, platforms are prime social structures to 159 exacerbate some particularly adverse practices that can have costly social consequences (e.g., Lam & Seidel, 2020)72. Though this dissertation has primarily taken a strategic management framing, there are indeed crucial higher-level implications of the research with respect to the sociology of platforms. As platforms increasingly permeate economic life, so too does it pervade scholarly conversations around topics such as employment relations, gig work, and economic and social inequality in general. In this arena, the discourse—academic or otherwise—is overwhelmingly grim. Platforms are framed as accelerants to social and economic disparity (Schor & Attwood-Charles, 2017), precarious work (Muntaner, 2018), and are even credited as an avenue for modern wage slavery—particularly for already disadvantaged groups (Lewis et al., 2015; Montgomery & Baglioni, 2021). Indeed, assessing the externalities of social and economic organization are more important than ever given the broader climate; or more technically, climates (e.g., environmental, economic, social, etc.). Just as the latent ills of the industrial era are only recently being managed, we must be especially vigilant with respect to what platforms bring. The spillover effects of a platform-centric world, coupled with the potential for network lock-in effects can indeed spell serious consequences for the trajectory of societal and global inequities. While platforms can arguably provide opportunities and avenues for such trends, there is no reason to believe that platforms inherently cause undesirable societal impacts. After all, we 72 A recent example of moral hazard stemming from "get big, fast” approaches in the classic firm context are the 2023 bank failures (e.g., including Silicon Valley Bank, Signature Bank, etc.). While the “privatizing profits, socializing costs” rhetoric is well-embedded into this era’s socioeconomic Zeitgeist—and particularly when it comes to financial institutions—these same concerns are exacerbated when platforms prioritizing quantity over quality are selected and rewarded by risky investment regimes. In such cases, costs may be directed to and absorbed by those that are already exploited and disadvantaged (e.g., Muntaner, 2018). 160 must not forget that the platform—objectively—is ultimately an organizational form. Just as the discourse highlights certain platforms for their direct negative societal impacts, others are known to provide innovative conveniences. Oftentimes, the societal shifts are nuanced: restructuring distributions (e.g., of power, resources, etc.) among participants, and within industries (Schumpeter, 1942). In their recent review, Vallas and Schor (2020) highlight that—despite platforms’ indisputable prominence—the future regime(s) of platform organization is yet to be determined. They offer different potential paths—ranging from predatory-exploitative to the cooperative-user-empowering. Given this, it is also worthwhile to discuss the relationship between platform practice and research. While the relationship is oftentimes framed as a practice-research divide (i.e., with research lagging), it is important to recognize that the relationship remains a reciprocal one. Therefore, a scholarly shift towards network-structural views can also serve to redirect the prescriptive rhetoric around platform management. Specifically, this dissertation’s findings promote a more community-oriented resilience-focused strategic approach. It is easy to take for granted the current platform structures around us. Google search, arguably the exemplar platform of all platforms, rose to prominence by exploiting a component organizing algorithm known as PageRank. PageRank is essentially a centralization optimizing approach. Many platforms also employ algorithms exploiting centrality (i.e., rich-get-richer) approaches. If organizing approaches reflect the classic “medium is the message” adage, what would the world look like if platform organizing policies followed a resilience-optimizing, community-empowering, approach?73 73 It is worthwhile to consider how even those in such strong central positions, such as Google, can be threatened quickly by technological leapfrogging (e.g., Schumpeter, 1942). The chatGPT phenomenon, for example, can 161 This dissertation joins a growing movement in the platform management literature focusing on platform networks’ internal dynamics (Lee et al., 2006), while also rejecting assumptions around single-platform lock-in. When platform membership is barrier-free, the quality of platform networks takes a central role. As this dissertation’s analyses suggest, platforms that organize dense clusters of activity (i.e., communities, etc.) incur an advantage to future activity. This simple kernel can shift the power balance from the platform sponsor totality that is currently espoused towards that of communities. This dissertation’s views contradict prevailing notions around monolithic market-cornering platforms; and suggests that an insurmountable power imbalance between large platforms and their participants need not be presumed, particularly in a paradigm without barriers to multi-platform participation. Indeed, if communities can organize and mobilize freely across platforms (cf. Lee et al., 2006), then perhaps the opportunity to regulate power imbalances and negative externalities can emerge from the bottom-up. Perhaps the proliferation of unregulated platform organizing will create the conditions for some counterbalancing organizational form paralleling the union to the 20th century firm. Time will tell. Platform executives adopt a plethora of ecological vernacular around “keystone” firms in “ecosystems” consisting of “symbiotic” participants, and the like. The terminology is not misplaced, as ecology provides a fitting analogy for the platform organizing context. Like most management fashion (e.g., Abrahamson, 1996), however, this vernacular risks disappointment if not substantiated; beyond mere buzzwords. That said, it is only a matter of time until an potentially surpass Google’s dominant position. Interestingly enough, the API model of training and distribution that chatGPT is building relies much less on centralization; which shifts the thinking in this area. 162 ecological network approach to strategic platform management is formalized. Hopefully, this dissertation pushes things along. On that vein, I advise platform executives and administrators to keep two key ecological points in mind. First: do not take network effects for granted. Platform networks are complex and nuanced. Strategically managing platforms should go beyond aggressively growing its network. Platform administrators with access to valuable data should leverage the vast trove of network ecological concepts to analyze and understand how activity is organized from a topological (i.e., structural) perspective—and how this impacts key outcomes. Supporting research in this area can be fruitful for scholars and managers alike. Second: be mindful of impact. While within-platform network externalities remain a key strategic imperative, platform administrators must also be cognizant of their own externalities (i.e., spillover effects). If social organizations are the engines of economies and society, platforms place us on the fast-track. Given our current climate, it is frightful to imagine platforms leveraging some aspects further (e.g., Vallas & Schor, 2020). Indeed, platforms are prime contenders for exasperating some of the ills of classic business, such as generating (potentially precarious) value through the obfuscated exploitation of select groups (e.g., Lam & Seidel, 2020; Muntaner, 2018). As platform organization achieves further prominence and undertakes this key moment in modern history, the executives and entrepreneurs at the helm must embrace their role in shaping the path at this critical junction (Vallas & Schor, 2020). 163 Conclusion While topological concepts continue to garner ongoing development within the broader network sciences (e.g., Bianconi, 2021), I take an introductory approach to outlining more general implications within a platform network context. More specifically, I highlight how connectance, centralization, clustering, centralized clustering, and cross-functionality can characterize network integration and, through it, provide valuable insight into the trajectory of network activity. Though far from incorporating the cutting edge of network science, this approach fits this dissertation's goal of synthesizing a network dynamic view for platform analysis. This dissertation’s contributions reveal a large and promising frontier for platforms research. By addressing the growing need to formalize network dynamics in order to more comprehensively understand platforms, this dissertation lays an important and potentially rich groundwork for future platforms research. In Chapter 2, I allude to the platform literatures’ path dependence and being imprinted by the platforms of the time. Although it is difficult to speculate how platforms research will continue to progress, it remains worthwhile to reflect on some possibilities. It is plausible that research streams will continue to stay in their respective lanes—with economics maintaining incremental progress over platforms as market intermediaries and the organizational theory literature continuing with platforms as hierarchies (e.g., industry infrastructures and technological architectures). Indeed, organizational theory itself suggests that these particularly large and established fields would be subject to stronger inertial pressures and resistance to change (e.g., Hannan & Freeman, 1977, 1984). However, a couple of convergence points hold promise. Regardless of its tendency towards platforms’ competitive aspects, the strategic management literature indiscriminately 164 incorporates theory and perspective from multiple literary streams (e.g., McIntyre & Srinivasan, 2017). As well, the information systems literature exhibits openness to a broad plethora of platform perspectives and topics (e.g., Möhlmannn et al., 2021; Rai et al., 2019; Sandberg et al., 2020; Wang, 2021). In addition to being home to key topics such as digital platform boundary management (e.g., Cenamor & Frishammar, 2021; Eaton et al., 2015; Ghazawneh & Henfridsson, 2013), major information systems outlets’ openness to publishing broadly on digital platforms positions its own community—rather elegiacally—as a boundary object in its own right. In doing so, it encourages broad collaboration across disciplines (e.g., Bonina et al., 2021; Ceccagnoli et al., 2012; Hukal et al., 2020; Parker et al., 2017) as well as a wider breadth of scholarly generativity in general. With its advantageous position in digital platforms research, it is easy to imagine the information systems field as the emergent epicentre for digital platforms research. In many ways, the story draws a parallel to the organizational theory discipline’s own rise to prominence (Davis, 2015). While organizational theory demarcated a clear and legitimate space to flourish by drawing a typological boundary between hierarchies and markets (Coase, 1937; Simon, 1991), the information systems’ own academic moat over platforms research ought to be more precarious than it may first appear. Indeed, the term “moat” may not be appropriate at all, particularly when the range of platforms research within the “primary” streams (i.e., economics and technology management) appear constrained by the structural inertias facing old and large social organizations in general (Hannan & Freeman, 1984). Just as economics should acknowledge that markets are increasingly organized by digital platforms, organizational theory should also accept that social organization is increasingly maintained in market-like form by the same digital platforms. This trend will transform society and social research. Will organizational 165 theory support another seemingly mismatched wing (i.e., platform-organized markets) in its paradigmatic house of wonders (e.g., Davis, 2015); or perhaps information systems is the more promising field for platforms scholarship to flourish, unfettered. Perhaps fields that can successfully organize research communities (i.e., network clusters) will foster greater activity. My own formal introduction to organizational theory began with a simple excerpt from Organizations and Markets (Simon, 1991). The first section, titled “The Ubiquity of Organizations,” describes a mythical Martian visitor that can perceive social structures using special equipment. The conveniently colour-coded social world is visualized as one dominated by blue-veined green masses, representing firms. Inside the green globs are people hierarchically connected by the blue veins, denoting authority. The green globs are also connected. They are connected by red lines representing market transactions. The Martian would report a social world consisting of “`large green areas interconnected by red lines.’ It would not likely speak of a `network of red lines connecting green spots.’” (p. 27). What would a visit today look like? The scene would be a rapid light show of yellow lines. Upon closer inspection, the yellow lines are just familiar red lines enveloped in a glow of green74. They are instant market transactions mediated by organizations. The green-glowing red lines are not only connecting green masses, but—more noticeably—people. Moreover, the people connected by these augmented transactions are not residing inside the green globs. Instead, they carry a red device that blinks yellow (actually, glows green) before these new organization-mediated market transactions occur. This process of rapid authentication starkly contrasts the pulsating blue veins 74 Red and green combine to appear yellow. 166 of authority preceding any major activity in the green blob world of old. The Martian would report a social world consisting of this new form of organization-mediated market transaction. They would speak of a platform world. Simon’s Martian excerpt encapsulates the discovery and intrigue awaiting social scientists, and particularly organizational scholars. The otherworld perspective-taking reminds researchers to not take things for granted, and that a rich social tapestry awaits—even with high levels of (colour-coded) abstraction. The special equipment embodies theoretical lenses. Organizational theorists have developed many great organization-centric apparatus to view the social world. More than three decades have passed since Organizations and Markets (Simon, 1991). Organizational scholarship staked a claim on the “large green spots” dominating the social world, and flourished. What of the current social world, with its strange new colours? This dissertation highlights taken for granted theoretical assumptions limiting platforms research. Another barrier to advancing platforms research is taken for granted assumptions around scholarly scope. What does organizational scholarship entail? There is a taken for granted assumption that the scope of organizational scholarship is limited to organizations. What is an organization? An organization is generally equated to a formal hierarchy (e.g., firms). Are organizational scholars limited to hierarchies—the green matter in Simon’s excerpt—or are they in the business of social organization more broadly? I take the stance that it is the latter. As a result, organizational scholarship requires apparatus to understand the strange yellow lines that increasingly come to organize our social world. This dissertation is my attempt. Regardless of how platforms scholarship mobilizes in the future, this dissertation surmounts a key bottleneck confining platforms research and initializes a formal framework for dynamic network analyses. The generative potential of this network dynamic framework is 167 nontrivial. The approach itself readily welcomes expansion via increasing analytical specificity. With slight modifications, the framework can explore weighted network analysis, overlapping networks, component-centric dynamics spanning multiple networks, variations on topological properties, topological evolution, multi-level analysis, boundary conditions, and alternate outcomes; to name a few of the many possibilities. As well, the framework provides an open interface to study how upstream platform levers impact platform activity through the various topological features presented in this dissertation. Platforms function through their networks. This dissertation’s analyses provide details about how network organization can impact platform activity; but far more important, the architecture developed in this dissertation establishes a formal lexicon to advance a network dynamic paradigm for platform analysis. The network dynamic approach introduced in this dissertation holds the potential to redefine platform management. With continued development, lasting implications can emerge for scholars, managers, and society more broadly. Scholars have a highly generative formal framework to build on. Managers can readily adapt this dissertation’s approach to measure various network structural facets and identify opportunities for greater structural integration on their own platforms. In this era of exceedingly atomic datafication, platform managers can also administer public institutions. 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Whitepapers are typically produced for ICOs and applications involving significant levels of capital investment. As a result, this variable is limited to contracts that are more likely to realize higher levels of overall size, activity, and value75. In order to construct a mapping of the contract space, researchers can use Google TensorFlow software to apply doc2vec to the library of whitepapers. doc2vec is based on word2vec (Mikolov et al., 2013), a machine learning approach that inputs a large corpus of text and outputs the component words as a set of n-dimensional vectors, following the learning process76. When the word vectors are mapped onto a vector space, similar words cluster together in closer proximity. doc2vec introduces document level vectorization to word2vec, and can be conceptually likened to adding fixed effects to regression modeling. In other words, document 75 While concerns around range restriction and measurement on the dependent variable are valid, the majority of deployed contracts realize little to no activity and size—and subsequently little variance in activity and size—throughout their existence. Moreover, the repeated measures design partly offsets such concerns as many contracts are observed during time periods of low activity and size (e.g., contract creation), but also realize growth and decline. Furthermore, the design of this study necessitates higher levels of activity in order to appropriately measure independent variables. 76 Explaining the full process of doc2vec is beyond the scope of this paper. 187 level effects are added to the process. Therefore, in addition to training and mapping a word vector space, a set of multidimensional document vectors is also output. Similar to the word2vec output, each document can be positioned in document space—with similar documents placed closer. Using the resulting map, researchers can calculate similarity as the Euclidean distance between any two contracts. The second component required to estimate niche crowding is the scale of each contract. While the doc2vec mapping represents the topological positioning of each contract, contract scale represents the area in the niche space that each contract occupies. A platform’s realized niche is proportional to its underlying network’s realized connections. The scale of a contract can be calculated by multiplying its realized connections during a given time by a scaling parameter. If the scaling parameter is too small, then positioning is emphasized and there will be no crowding for contracts that do not share identical positions. If the scaling parameter is too large then crowding will only emphasize contract scale, essentially becoming a ranking of contract scale; thereby muting the effect of positioning and (dis)similarity. Therefore, it is necessary to first establish a tenable scaling parameter representative of niche overlap. Niche overlap is established as the overlapping area between entities in a multidimensional resource space. In his paper on voluntary associations in a Midwestern US city, McPherson (1983) illustrates that different types of voluntary associations recruit members from a bounded range of two dimensions—age and years of education. The area of overlap in recruit characteristics represents the group of potential recruits that are viewed as the niche that both types of voluntary associations compete for. A potential recruit in the overlapping area can be viewed as being sought after by both types of associations, but only being taken in by one. The present context is different. Addresses can hold membership and participate in multiple 188 contracts. Therefore, one way of assessing the niche overlap of contracts is to use the niche profiles of addresses. An address’ set of contract affiliations can be used to indicate their niche. Researchers can determine the scaling parameter by identifying the contract with the highest realized connections (contract A). Next, they can identify the contract with which contract A has the most shared addresses with (contract B). Using the Euclidean distance and the overlap in addresses between the two contracts, solve for a scaling constant such that the radius of a contract (representing its scale) is the product of its realized connections during a given time period and the scaling constant. To solve for the scaling parameter, use two-dimensional Euclidean geometry to establish a two-circle intersection problem. The two-circle intersection problem involves three primary components, as illustrated in Figure A-A1: Figure A-1: Area of Overlapping between Two Circles of Different Sizes77 77 Source: http://mathworld.wolfram.com/Circle-CircleIntersection.html 189 The three primary components are the distance between the centers of the circles, d, and the respective radii of the two circles, R and r. Where d is determined by doc2vec mapping, R and r are determined by multiplying the scaling parameter with the number of realized connections a contract has for a given time period. To calculate the scaling parameter, first determine the area of overlap based on the proportion of addresses that are common to contracts A and B. Second, solve for the scaling parameter that equates to the area of overlap and corresponding Euclidean distance between the center points of the two circles given the number of realized connections for contracts A and B. Although this approach is somewhat crude, the band of tenable values for the scaling parameter is lenient due to the fact that it scales all contracts equally. The relative ordering of contracts’ niche overlap will remain intact so long as the scaling parameter is not too low so as to eliminate variance from niche crowding (i.e., almost no overlap) and not too high so as to negate the effects of contracts’ (dis)similarity (i.e., almost full overlap). In other words, there is not a single “perfect” scaling constant, but rather a fairly wide range of tenable scaling constants. Finally, the number of realized connections are multiplied by the scaling constant to calculate each contract’s “niche radius.” Using the contract niche radius and pairwise matrix of contract distance scores, calculate each contract’s niche crowding as the summation of the proportion of area overlap between the focal contract, i, and all other contracts, j, drawn from a set of contract radii, S, such that Si = {rj : rj + ri > dij}. In other words, the niche radius of contracts that overlap with the focal contract (i.e., rj + ri > dij) are used to calculate niche crowding, which is formally specified as: 190 𝐶௜ =1𝜋𝑟௜ଶ෍ ቆ𝑟௝ଶ𝑐𝑜𝑠ିଵ ቆ𝑑௜௝ଶ + 𝑟௝ଶ − 𝑟௜ଶ2𝑑௜௝𝑟௝ቇ + 𝑟௜ଶ𝑐𝑜𝑠ିଵ ቆ𝑑௜௝ଶ − 𝑟௝ଶ + 𝑟௜ଶ2𝑑௜௝𝑟௜ቇ௝∈ௌ−12 ට(−𝑑௜௝ + 𝑟௝ + 𝑟௜)(𝑑௜௝ + 𝑟௝ − 𝑟௜)(𝑑௜௝ − 𝑟௝ + 𝑟௜)(𝑑௜௝ + 𝑟௝ + 𝑟௜)ቇ where radius rj is from a set of radii Si representing all contracts that overlap with contract i. The radii set and their corresponding distances from contract i are used to calculate the overlap of the two intersecting circles with radii rj and ri given distance dij using the equation for calculating the area of two overlapping circles, which is in parentheses to the right of the summation symbol, Σ. The summed areas are finally divided by the area of the focal contract’s niche area. Higher values of Ci correspond to higher niche crowding. It is also possible to code an alternate version of niche crowding based closer to established common-resource based approaches (McPherson, 1983; Podolny et al., 1996). More specifically: operationalizing niche overlap in terms of contracts’ shared addresses during a given time period. Coding niche crowding according to the proportion of common active addresses for all contract pairs has several notable differences. First, unlike conceptualizations of niche crowding which emphasize incorporation of resources from the environment, an open platform context such as Ethereum allows near frictionless mobility between contracts. In a context where actors can access and freely interact with many contracts, actual activity across multiple contracts can be viewed as a more direct and conservative measure of niche overlap. The common membership conceptualization of niche overlap can be representative of multihoming across similar contracts. Furthermore, not relying on whitepapers allows analysis to include a larger set of contracts, addressing range restriction concerns. 191 The calculation of the alternatively coded, overlapping address based, niche crowding variable is simpler than the distance-based version: 𝐶௜ᇱ =1𝑐௜෍|{𝑣௞ ∶ 𝑣௞ ϵ 𝑉௜}|௞ஷ௜ such that v represents addresses and where C’i is the summation across all contracts, k, excluding the focal contract, i, of the count of the set of (|{…}|) addresses such that ({𝑣௞ ∶) the addresses are elements in the set of addresses belonging to contract i (𝑣௞ ϵ 𝑉௜), divided by the number of realized connections for contract i during a given time period. In other words, the alternative measure of niche crowding is the aggregate of all pairwise contract addresses, divided by the scale of the contract. However, this is not a completely appropriate approach because some contracts compliment—even depend upon—others and realize significant overlap in their user base. Some platforms use several specialized contracts in a single application. However, these contracts in aggregate constitute the platform, and it is through their complementarity that any single contract is able to realize its commensurate size and activity levels. Therefore, this is not a completely inappropriate approach to measuring niche crowding either. Even though a particular contract belonging to the same platform can appear to be fully overlapped by another contract on the same platform, the positive network effects between contracts (e.g., different markets on the same platform) can produce a net positive effect through scaling, which offsets crowding from external platforms. It may very well be possible that the most active platforms belong to a network of complementary platforms which exhibit higher levels of within-network crowding but lower between-network as a result of the platform network’s superior scale, and 192 commensurate network effects. Using these two versions of niche crowding lends a degree of triangulation to the overall analyses.
Thesis/Dissertation
eng
Business Administration - Organizational Behaviour and Human Resources
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Seidel, Marc-David
van Jaarsveld, Danielle Dorice
Toward a network dynamic view of the platform
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