UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

An analysis of three models proposed to account for choice behavior in two person non-zero sum games Thorngate, Warren Bayley 1968

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1968_A8 T46.pdf [ 4.9MB ]
Metadata
JSON: 831-1.0104348.json
JSON-LD: 831-1.0104348-ld.json
RDF/XML (Pretty): 831-1.0104348-rdf.xml
RDF/JSON: 831-1.0104348-rdf.json
Turtle: 831-1.0104348-turtle.txt
N-Triples: 831-1.0104348-rdf-ntriples.txt
Original Record: 831-1.0104348-source.json
Full Text
831-1.0104348-fulltext.txt
Citation
831-1.0104348.ris

Full Text

AN ANALYSIS OF THREE MODELS PROPOSED TO ACCOUNT FOR CHOICE BEHAVIOR IN TWO PERSON NON-ZERO SUM GAMES by WARREN BAYLEY THORNGATE •B., University of California, Santa Barbara, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Arts i n the Department of Psychology We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1968 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C olumbia, I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and Study. I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u rposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada i ABSTRACT An experiment was conducted to te s t the adequacy of three models of game playing behavior i n accounting f o r choices made by eighteen females i n three non-zero sum games. Data were obtained for t e s t i n g a Markov model, a Subjective Expected U t i l i t y model and a Rational Motive Pursuit (ne" Stochastic Choice) model. Results indicated some support f o r a l l models, however the Markov model appeared to predict the data most accurately, the R.*!.P. model less accurately and the S.E.U. model l e a s t accurately. Much of the data were interpreted In terms of each model and a t h e o r e t i c a l synthesis of them was proposed. I i TABLE OF CONTENTS Page Abstract i Table of Contents 11 L i s t of Tables l i t Acknowledgment v l Chapter 1: Introduction 1 Chapter 2: Three Models of Game Playing Processes 6 The Markov Process Model 6 The Subjective Expected U t i l i t y Model 11 The Rational Motive Pursuit Model 15 Chanter 3: Experimental Method 19 The F i r s t Session 19 The Second Session 23 The Third Session 30 Chapter 4? Results and Discussion 34 Sone General Results 34 Results and Discussion of Markov Process Model 38 Results and Discussion of Subjective Expected U t i l i t y Model 48 Results and Discussion of Rational Motive Pursuit Model 54 Chapter 5; Synthesis 79 Bibliography 87 LIST OF TABLES Average number of choices in each of Session Two's games Average number of choices in the games of Session Three Analysis of Variance summary table of the number of A or X choices in the games of Session Two Analysis of Variance summary table of the number of A or X choices in the games of Session Three Actual response proportions and predicted response proportions (underneath actual) of each dyad for the JO-P game of Session Three Actual response proportions and predicted response proportions (underneath actual) of each dyad for the J-R game of Session Three Actual response proportions and predicted response proportions (underneath actual) of each dyad for the J-OT! game of Session Three Average transition matrices and starting propensities for each game of Session Three The probability of a person cooperating on a t r i a l following each of the four possible joint responses in the games of Session Three The number of cooperative responses given by members of five dyads in the J-R game *7ho either cooperated or competed on the first t r i a l i v Page XI The p r o b a b i l i t y of persons who cooperated on t r i a l one of the J-R game cooperating on the t r i a l following each of four possible j o i n t responses 47 XII F i r s t t r i a l and o v e r a l l responses of persons with A or X dominance, no dominance, or S or Y doninance on the games of Session Three 4fi XIII T^ ean subjective p r o b a b i l i t y estimates of other choosing A or X given by persons i n each game of Session Three following 0, 1, 2, or 3 A or X responses given by other i n the p r i o r three t r i a l s 49 XIV The numerical representation of u t i l i t i e s f o r each of the four possible j o i n t responses f o r those persons i n each game of Session Three with no dominant s o l u t i o n and with usable higher ordered metric data 51 XV The number of confirmed and unconfirmed S.E.U. predictions f o r each person of Session Three with an av a i l a b l e numerical representation of t h e i r outcome u t i l i t i e s 53 XVI P r o b a b i l i t y estinates of being i n one motive state derived from Subjects' behavior i n the games of Session Two 55 XVII Motive state p r o b a b i l i t y estimates derived from each set of two games i n Session Three 56 XVIII The proportion of A or X choices predicted from three sources and observed i n the games of Session Three 56 XIX ??otive state p r o b a b i l i t y estimates derived from f i r s t t r i a l choices of Subjects i n the games of Session Three 57 XX Predictions of A or X choice proportions on the f i r s t t r i a l of Session Three's games 58 XXI Collapsed t r a n s i t i o n matrices f o r the games of Session Three 60 The proportion of own, joint, relative, and other reasons given in the games of Session Two The proportion of trials on which each reason (A-K) was used and pursued by an A. or X, or B or Y choice in the games of Session Three The proportion of times reasons A-F were rationally pursued when a rational solution existed The probability of eacb reason being given following each type of outcome in the games of Session Three The average probability of & Subject continu-ing to use an own, joint or relative gain * reason on the tr i a l following a cooperative or competitive choice by the other Maximum likelihood motive state probability estimates, derived predictions and observed proportions of cooperative choices for Cooperators and Competitors in the games of Session Three Reasons given on the first t r i a l of the J-F game by members of dyads who cooperated and competed on the first t r i a l The proportion of reasons used and the proportion followed by a cooperative choice for five Cooperators and for five Competitors averaged over trials 2-20 of a l l the games of Session Three The propensities of Cooperators and Competitors to select various reasons following each outcome type averaged over a l l games of Session Three v i ACKNOWLEDGMENT I s i n c e r e l y wish to thank Drs. G i l l i a n Petrusic and Pobert Knox f o r t h e i r enthusiasm and kind assistance i n guiding and reviewing t h i s e f f o r t . CHAPTER 1 INTRODUCTION One of the most pervasive phenomena of s o c i a l behavior i s that of Interpersonal c o n f l i c t . Recently, a number of mathematical models have been formulated i n an attempt to account f o r various aspects of t h i s phenomenon. This thesis presents an attempt to t e s t e m p i r i c a l l y a Markov model, a Subjective Expected U t i l i t y model and a Rational Motive P u r s u i t model and to i n t e r p r e t r e s u l t s i n the l i g h t of each using one experimental paradigm of interpersonal c o n f l i c t , a two person game. Consider the following minimal s o c i a l s i t u a t i o n . Two persons (1 and 2) are brought together and each given two a l t e r n a t i v e choices. Let A and B be the choices a v a i l a b l e to person 1, X and Y those a v a i l a b l e to person 2. Let AX, AY, BX and BY denote the four possible outcomes (O^S) which could j o i n t l y occur as a r e s u l t of both persons simultaneously s e l e c t i n g one of t h e i r i n d i v i d u a l a l t e r n a t i v e s . F i n a l l y , l e t pfj(AX), p f i ( A Y ) , p f ^ B X ) , and pfi(BY) be the payoffs to person 1 i f AX, . . ., BY should occur, and l e t p f 2 ( A X ) , p f 2 ( A Y ) , p f 2 ( B X ) , pf 2(BY) be those payoffs accrued by person 2 i f these p a r t i c u l a r outcomes should occur. Such a s i t u a t i o n i s commonly ref e r r e d to as a two person, two choice game (see Luce and R a i f f a , 1957). Within the l a s t decade numerous experiments have been performed i n v o l v i n g t h i s s o - c a l l e d "game" paradigm as i t provides a r e l a t i v e l y c o n t r o l l e d s e t t i n g f o r the study of interpersonal choice behavior from 2 which analogies may hopefully be drawn to the less c o n t r o l l e d environs (see, f o r example, Rapoport, 1962). A good amount of variance has been observed both w i t h i n and between experiments i n the proportion of p a r t i c u l a r choices made by Subjects. 1 This variance has been shown to r e s u l t from f i v e generic sources: 1) differences between Subjects; 2) differences between games; 3) differences over time; 4) i n t e r a c t i o n s between Subjects, games and time; and 5) E r r o r . Between-Subject differences such as sex (Rapoport and Chammah, 1965), n a t i o n a l i t y (McClintock and McNeel, 1968), p r i o r i n t e r a c t i o n s (McClintock et a l , 1963) and personality (McClintock et a l , 1963; Deutsch, 1960) have been shown to a f f e c t c onsistently the o v e r a l l proportion of responses leading to maximized j o i n t payoff (where pf^O^) + p f 2 ( 0 ^ ) i s maximum) i n c e r t a i n non-zero sum games (where pf^O^) - pf2(0 i) 4 0). Consistent differences i n t h i s o v e r a l l proportion have also been shown to r e s u l t from differences between games, such as the d i f f e r e n t i a l payoffs given to each person f o r the j o i n t s e l e c t i o n of a p a r t i c u l a r outcome (Rapoport and Chammah, 1965; Minas et a l , 1960; Deutsch and Krauss, 1962), the information given to-'persons about t h e i r own and the other's payoffs (McClintock and *Yet i t has been noted that the d i s t r i b u t i o n of a p a r t i c u l a r response proportion defined as "cooperative" (where pfi(0j[) + pf2(0^) i s maximized) tends to be skewed p o s i t i v e l y , with fewer cooperative responses made than might be expected i n "analogous" non-Game s o c i a l s i t u a t i o n s (see Knox ,an^ iD^uglas, 1968). 3 McNeel, 1968; McClintock and Messick, 1968; Messick and Thorngate, 1967), and the amount of communication allowed between the two persons (Deutsch and Krauss, 1960; Loomis, 1959). Finally, choice proportions have been shown to di f f e r over time as a particular game is repeatedly played, though the nature of this change is dependent upon the nature of the game and persons playing i t (Rapoport and Chammah, 1963; McClintock and McNeel, 1968). At least three good c r i t i c a l reviews of these findings exist (Gallo and McClintock, 1965; Becker and McClintock, 1967; Rapoport and Orwant, 1962) and the reader i s advised to refer to these for more detailed synopses. For purposes of this thesis only one aspect of this accumulation of research findings need be noted: the extreme paucity of experimental efforts which focus on investigating the processes by which these Subject, game and time differences are presumed to occur. Ten years of experimentation with the game paradigm have resulted i n an amassing of s t a t i s t i c a l relationships between some specified independent variable and some averaged index of game playing behavior a l l but devoid of anything more than casual discussion of those intervening processes assumed to contribute to these relations. Research i n the area appears to have approached a sort of social psychological s t r i c t behaviorism, with the game board a sequel to the lever box as i t s a l l but singular instrument of investigation. This does not imply that the research has, in effect, been wasted. It has, at very least, been beneficial i n demonstrating that choice behavior i n a game can be changed or influenced by specific variables. And these influences appear more than roughly concordant with what one would expect 4 i n analogous non-laboratory situations (Thorngate, 1968). Such observations, alone, should provide sufficient justification for any future experimenta-tion of a more process-oriented nature. Unfortunately, there i s no readily available or unanimously acceptable definition of a process. Intuitively, i t seems reasonable to assume that a process '"converts" or ''transforms" some entity, referred to as an input, into some other entity, referred to as an output, and this shall be assumed here. Numerous classifications of transformations and distinctions between transformations have been made (see, for example, Ashby, 1963). One relevant distinction i s that made between what nay be called an "E~process': and what may be called an 3,S-process." An E-process i s one which ultimately converts types or quantities of energy into other types or quantities of energy. Such processes include a l l animals and machines. An S-process i s one which converts symbols into other symbols. Such processes include grammars, logics, and mathematics. Game playing i s an E-process by which light energy reflected off the game board and striking a player's eye i s converted into the muscular energy required to make a specified "move" or choice. Numerous S-processes may be fomulated which transform symbols in a manner concordant with any number of aspects of this E-process. Three of the S-processes (hereafter referred to as models) which could be utilized to account for various aspects of game playing behavior are a Markov model, a Subjective Expected U t i l i t y model and a Rational Motive Pursuit model. They differ in at least two ways; f i r s t , i n what they assume to be relevant aspects of the game playing "process" Inputs, and second, i n how they assume these 5 aspects are "processed1 into game playing behavior. In order to determine nore precisely the nature of these models and their differences the follovring discussion is presented. CHAPTER 2 THREE MODELS OF GAME PLAYING PROCESSES The Markov Process Model (see Suppes and Atkinson, 1960; Burke, 1959; Rapoport and Chammah, 1965). Assume there are n t r i a l s of a p a r t i c u l a r game and assume that on any given t r i a l (k) the two persons (dyad) playing the game can j o i n t l y s e l e c t one of the four outcomes: AX, AY, BX or BY. Then a process by which they j o i n t l y s e l e c t outcomes from t r i a l to t r i a l i s a Markov process i f f : 1) P(0 l f k>* = p ^ j A X ^ M A X ^ ) + ^Vk'^k-l^w + ? ( 0 i , k l B X k - i > p < B W + p c V ^ V i ^ W and 2> p ^ k ' - ^ W ' p ( 0 i , k l A Y k - i > ' p ( 0i,klB Xk-i> " * * ( 0 i , k l B Y k - i > a r e constant f o r a l l n-k2l. A Markov process of the above game can be summarized i n the following matrix form: *read, "the p r o b a b i l i t y of outcome 1 on t r i a l k" 7 t r i a l k AX t r i a l AY k + 1 BX BY AX P r l l P*12 P r 13 P ' l i * AY P*21 p r 2 2 p r 2 3 pr 2 i» BX P*3X P r 32 P*33 pr34 BY P ^ l p r i l 2 Prit3 Pr«t«t Suppose that on the f i r s t t r i a l a p a r t i c u l a r dyad w i l l choose AX, AY, BX or BY with given p r o b a b i l i t i e s ; that i s , suppose op the f i r s t t r i a l p(AXi), . . ., p(BYj) i s known. In order to determine how these p r o b a b i l i t i e s change on t r i a l s 1 , 2 , . . ., n we simply employ formula 1) above; f o r example: pr(AX 2) - p r u • prCAXi) + p r 2 i • pr(AYj) + p r 3 1 • prCBXi) + p r ^ • pr(BYj) pr(AX 3) - p r n • pr(AX 2) + p r 2 i • pr(AY 2) + p r 3 i • pr(BX 2) + pTm • pr(BY ) and so f o r t h u n t i l the nth t r i a l . To determine to what extent game playing behavior of dyads can be accounted f o r by the Markov model i t i s f i r s t necessary to provide persons with a 2 x 2 game and l e t them play i t repeatedly, noting t h e i r t r i a l - b y -t r i a l behavior. This t r i a l - b y - t r i a l behavior could then be summarized i n a t r a n s i t i o n matrix to estimate p n » • • • > Pi»»* so that t h e i r choice on the f i r s t t r i a l could be combined with t h i s matrix to produce t r i a l - b y -t r i a l p r e d i c t i o n s . The predictions would then, of course, be compared to the ac t u a l behavior f o r ''goodness of f i t , " as i t were. To the extent that 8 the predictions were concordant with observed behavior the Markov process could be considered a tenable "explanation" of t h i s behavior. One l i m i t a t i o n of t h i s goodness of f i t t e s t should be noted i n passing, a l i m i t a t i o n which i s implied by the following theorem: Theorem: Let L be a matrix of response propensities on t r i a l n-1, and M, a t r a n s i t i o n matrix. Let Q be another response propensity ( p r o b a b i l i t y ) matrix on t r i a l n-1, and R, another t r a n s i t i o n matrix. Then, E[(L + Q) X ( M + R ) ] - E[LXM + QXR] i f f , LXM + QXR - LXR + QXh . Proof: E[(L+Q) X (M+R)] = (L+Q) X (M+R) -2 2 LXM + LXR + QXM + QXR 2 LXM + LXR + QXM + QXR _ LXM + QXR i f f 2 £jaf + LXR + QXM + QXR* = 2 (LXM) + 2 (QXR) LXR + QXM = LXM + QXR To become aware of whatever profundity e x i s t s i n t h i s theorem, assume that one dyad (#1) has a known p r o b a b i l i t y of choosing AX, AY, BX or BY on a p a r t i c u l a r t r i a l (n-1) summarized i n the following matrix: AX AY BX BY L = P i P 2 P 3 P«t 1.00 Assume, too, that t h e i r behavior can be w e l l described by a Markov process with t r a n s i t i o n matrix M. Suppose there i s another dyad (#2) with i t s own p r o b a b i l i t i e s of choosing AX, AY, BX or BY on t r i a l n-1: 9 AX AY BX BY p'l P*2 P \ and i t s own t r a n s i t i o n matrix R. To determine the p r o b a b i l i t i e s that dyad iti w i l l choose each of the outcomes on the next t r i a l (=n) one simply m u l t i p l i e s LXM; correspondingly the nth t r i a l p r o b a b i l i t i e s f o r dyad #2 are determined by m u l t i p l y i n g QXR. Presumably i t would be possible to get a better estimate of the s t a r t i n g p r o b a b i l i t i e s (pr(O^) on t r i a l 1) and t r a n s i t i o n p r o b a b i l i t i e s by pooling the data of these dyads. For example, to obtain our best estimate of the four response p r o b a b i l i t i e s on the f i r s t t r i a l , i t seems reasonable to average the response p r o b a b i l i t i e s on that t r i a l f o r a l l those dyads i n a p a r t i c u l a r condition. S i m i l a r l y , to obtain better estimates of t r a n s i t i o n p r o b a b i l i t i e s i t seems reasonable to average the t r a n s i t i o n p r o b a b i l i t i e s of a l l these dyads. The reasonableness of these propositions i s based on the assumption that i f each of two or more dyads' behavior can be described by a Markov process, so can t h e i r pooled (or averaged) behavior. The theorem j u s t put f o r t h shows t h i s to be a v a l i d assumption only under the condition given. This condition can be immediately s a t i s f i e d i n two ways: 1) i f the ( n - l ) t h t r i a l choice p r o b a b i l i t i e s are i d e n t i c a l f o r the dyads, i . e . , i f L - Q; or 2) i f the t r a n s i t i o n matrices are i d e n t i c a l for the dyads, i . e . , i f M = R. I f neither of these conditions i s s a t i s f i e d an unbiased pooled r e s u l t should not be expected. T r a n s i t i o n matrices have been shown to d i f f e r between dyads (see 10 Rapoport and Chammah, 1965). I f i t were possible to assume that the f i r s t t r i a l response propensities were i d e n t i c a l f o r each dyad, then t h e i r data could be v a l i d l y pooled regardless of how divergent t h e i r t r a n s i t i o n matrices might be. This assumption i s exceedingly d i f f i c u l t to t e s t , since the only estimate of s t a r t i n g propensities a v a i l a b l e f o r each dyad i s t h e i r behavior on the f i r s t t r i a l . Yet I t seems i n t u i t i v e l y i n c o r r e c t , as i t assumes that a l l persons "approach 3' the s i t u a t i o n In the same manner, that the s i t u a t i o n i n e f f e c t wipes out a l l i n d i v i d u a l d i f f e r e n c e s . There i s one obvious recourse: make i n d i v i d u a l predictions f o r each dyad by m u l t i p l y i n g i t s s t a r t i n g state i n t o i t s t r a n s i t i o n matrix and the r e s u l t into the t r a n s i t i o n matrix again, etc., f o r the number of t r i a l s i n the game. A f t e r these t r i a l - b y - t r i a l predictions have been made f o r i n d i v i d u a l dyads, then pool the predicted proportions for each t r i a l or group of t r i a l s , and compare with the actu a l pooled proportions. This method s h a l l be employed i n analyzing the Markov model. Again, we know that c e r t a i n i n d i v i d u a l d i f f e r e n c e s , time dif f e r e n c e s and game d i f f e r e n c e s , a f f e c t o v e r a l l game playing behavior, or symbolically we thus know: AI -»• AG.P.B. AG AG.P.B. AT »• AG.P.B. To the extent that a Markov process can account f o r these di f f e r e n c e s i n game playing behavior the following may be i n f e r r e d : AG • AM.P. -• AG.P.B. 11 Al v AM.P. • AG.P.B. AT • AM.P. • AG.P.B. The focus of Inquiry should then shift to the determination of how various AG's, AI's and AT's affect the "parameters" of a particular Markov process. This would be a trivial "shift," providing no new information, i f for every overall game playing proportion there existed one and only one Markov process which would produce i t ; but in fact there exists a host of Markov processes which could produce i t , or closely approximate i t , each potentially divulging some bit of insight into those things making persons play as they do. The Subjective Expected Utility Model (see Davidson, Suppes and Siegel, 1957; Becker and McClintock, 1967; Siegel, 1964). There are actually a number of SEU models, which vary from one another primarily in the restrictiveness of their assumptions (see Becker and McClintock, 1967). What a l l have in common is the generic conception that a person faced with a choice between a number of alternatives, each having at least one possible outcome, will utilize two types of information, 1) subjective values and 2)subjective probabilities, in making his selection. A subjective value, or ut i l i t y , of an outcome is conceived of as its personal "worth," "desirability," or "attractiveness." Operationally, i t is assumed that the utility of one outcome is greater than another i f the former is preferred to, or chosen over, the latter. Utilities are generally assumed transitive and, in the more rigid axiomatic systems, additive (see Tversky, 1965). They are also assumed to remain relatively 12 constant over time or at l e a s t to vary independently of i t (Davidson, Suppes & S i e g e l , 1957). Subjective p r o b a b i l i t i e s are considered to r e f l e c t the personal " b e l i e f " or "expectation" that a person possesses as to whether or not a p a r t i c u l a r outcome w i l l occur at the time of choice. They are u s u a l l y assumed to be monotonic increasing with " o b j e c t i v e " p r o b a b i l i t i e s and, l i k e objective p r o b a b i l i t i e s , are usually assumed to sum to u n i t y (see Edwards, 1962). I t i s also assumed that subjective p r o b a b i l i t i e s vary from t r i a l to t r i a l as some function of the accumulation of information on past events (see Savage, 1962). F i n a l l y , but perhaps u n r e a l i s t i c a l l y (see, f o r example, Becker et a l , 1964), u t i l i t i e s and p r o b a b i l i t i e s are assumed to vary independently of one another. Given these assumptions the subjective expected u t i l i t y of an a l t e r n a t i v e , A, i s defined as: n SEU(A) = I U(0 /A)p(0 /A) i - l That i s , the subjective expected u t i l i t y of A i s the sum of the U t i l i t y of each outcome i n A m u l t i p l i e d by the subjective p r o b a b i l i t y of the outcome occurring, given A. F i n a l l y , a l l SEU models assume that persons faced with a choice of two or more a l t e r n a t i v e s w i l l choose, or tend tc choose, that one having the highest SEU. I f two or more alt e r n a t i v e s have the same SEU each w i l l be chosen with equal frequency. Some SEU models assume that an a l t e r n a t i v e with the highest SEU w i l l be chosen e x c l u s i v e l y while others assume only that i t w i l l be chosen with a higher p r o b a b i l i t y than the others (Luce and Suppes, 1965). The l a t t e r w i l l be assumed here. In the game s i t u a t i o n described e a r l i e r the SEUs f o r person l ' s 13 alternatives on t r i a l k of a game are given by the equations: SEUfc(A) = U(AX)pk(X) + U(AY)pk(Y) SEUk(B) - U(BX)pk(X) + U(BY)pk(Y) The SEU model would predict that on those trials where SEU(A)>SEU(B), A would be chosen with higher probability than B; whenever SEU(B)>SEU(A), B would be chosen with higher probability than A. The model also dictates that i f U(AX)>U(BX) and U(AY)>U(BY) or i f U(BX)>U(AX) and U(BY)>U(AY) a condition referred to as dominance would exist and in this case A or B would be the dominant alternative, respectively. If a dominant alternative does exist i t would, of course, remain dominant over a l l subjective probability estimates and i t should be chosen with higher probability than the non-dominant alternative regardless of the subjective probability estimate existing at any time. These probability estimates should only be Influential in determining choice probabilities when no such dominant alternative exists. To test the adequacy of this model in accounting for game playing behavior, measurements of utilities and subjective probabilities are first needed. More than one means exist for experimentally estimating utilities (see Becker and McClintock, 1967). The one to be used here, known as the preference for gambles or PFG task, was originally developed by Siegel (1956). Basically, subjects are first required to rank order some set of entities or outcomes in terms of preference and then to indicate preferences for certain gambles between these entities. From their preferences for gambles a rank order of subjective distances between a l l pairs of entities (known 14 as a higher ordered metric) may be calculated. By employing an algorhythm developed by Goode (1964) a numerical representation of these higher ordered metrics, corresponding quite closely to an interval measure of ut i l i t i e s , may be determined. If a Subject's utilities for outcomes AX, AY, BX and BY are known and no alternative is found dominant then, by solving the two simultaneous equations presented above, the subjective probabilities p(X) for Subject 1 and p(A) for Subject 2 may be found such that the SEUs for each alternative are equal. Above this critical probability one alternative should be chosen more frequently than the other and below i t , the other alternative should be chosen more frequently. And again, i f one alternative is dominant i t should be chosen more frequently than the other regardless of the subjective probability estimate. In this experi-ment Subjects will be required to give trial-by-trial probability estimates of what the other person will choose on the next t r i a l . For those Subjects with a dominant alternative the relative frequency of selecting this alternative will be determined to see i f , in fact, i t was selected more frequently than the other. For those Subjects with no dominant alternative a test will be made to determine i f the prescribed alternative was, in fact, chosen more frequently than the other as their probability estimates fluctuated above and below the critical probability. To the extent that the predictions of the SEU model can account for the observed data the following may be inferred: A Game •+ ASEU • ABehavior 15 AIndividual -*• ASEU • ABehavior A Time •> ASEU + ABehavior I f t h i s inference i s successful i t w i l l be f r u i t f u l to look further i n t o the components of the SEU process, i n order to determine, f o r example, the u t i l i t y of various components or aspects of outcomes or the r e l a t i o n between objective and subjective p r o b a b i l i t i e s . The Rational Motive Pursuit Model ( o r i g i n a l l y c a l l e d the Stochastic Choice Model, see Messick and McClintock, 1968). In most two person, two choice, non-zero sum games persons are displayed both t h e i r own payoffs i n each outcome and the payoffs of the other person. Let ?i(.0±) and P 2 ( 0 j ) be the payoffs to persons 1 and 2 of outcome 0^, r e s p e c t i v e l y . F i r s t , assume that on any t r i a l a person may " d e s i r e " to choose that outcome which e i t h e r maximizes the maximum (max-max) or maximizes the minimum (minimax) of the following three outcome a t t r i b u t e s : 1) h i s own gain = P i f a j ) f o r person 1, ?2(Q±) f o r person 2; 2) the j o i n t gain » P^C^) + P 2(0 ; l) 3) the r e l a t i v e gain = Pi(Oj) - P 2 ( 0 i ) f or person 1, P 2 ( 0 ± ) - P i ^ ) f o r person 2 or that he may be 4) i n d i f f e r e n t , i n which case he chooses h i s a l t e r n a t i v e s with equal p r o b a b i l i t y . Second, assume that the p r o b a b i l i t y of a person being i n any one of these motive states on a p a r t i c u l a r t r i a l of the game i s constant over time and independent of previous outcomes. T h i r d , assume 16 that i f a person is in either of the first three motive states he will rationally pursue i t (choose its max-max or minimax solution) i f and only i f there is a rational solution, and that i f none exists for that motive state he will randomly select from the four possible states until he enters a motive state which does have a rational solution or until he enters the Indifferent state and randomly chooses one of the alternatives with equal probabilities. These three assumptions shall be referred to as the motive assumption, the independence assumption and the rationality assumption, respectively. Together they constitute the basis of the Rational Motive Pursuit (or RMP) model. There seem to be two generic means of testing the adequacy of the RMP model in accounting for game playing behavior. The more direct method would be to obtain trial-by-trial reports of a person's reasons for choosing what he is about to choose and to determine 1) to what extent he selected the rational solution to a reported motive when i t existed, and 2) whether the probability of reporting to be in a motive state remained constant following a l l possible outcomes. The less direct method would consist of providing persons with a number of games each having clearly defined, rational solutions of the appropriate motives; to estimate the probabilities of being in each motive state using the data from some of these games; and then to predict how the persons should behave in the remaining games given these estimated parameters (the technique used by Messick and McClintock, 1968). The direct method could potentially provide considerably more information about the RMP model, for a given number of games played. 17 For example, an analysis of Subjects' reports of only one game could potentially provide a test of the rationality and trial-by-trial motive independence assumptions and would determine to what extent the "max-max" and "minimax" criteria for rationality were pursued. However the more direct test seems to present persons with a more intellectually imposing task than the less direct test (which, indeed, requires nothing of them other than pushing buttons). As a result any non-supportive direct evidence for the validity of this model could therefore be interpreted as a failure of reporting the motives accurately rather than failing to "process" the reported motives into predicted behavior. The problem of selecting the more appropriate test of this BMP model therefore reduces to the problem of choosing between the "distorted refinement" of the direct method or "straightforward crudity" of the indirect one. As a solution, both tests shall be employed and evaluations of their appropriateness made after the extent of their discrepancies from the observed data and from one another (if any) have been determined. Here also, to the extent that the RMP model can account for the observed game playing behavior, the following may be inferred; Al -+ Ap (Motives) -> AB AG > Ap (Motives) •+ AB The model does not predict any changes in behavior (AB) over time, due to the trial-by-trial independence of motive selection assumption. A change in behavior over time may be observed, thus violating the independence assumption. But such a violation does not necessarily dictate the failure of the construct "Motive" to account for the data; 18 its failure could only be shown by failure to account for AI • AB and AG ——• AB differences. To account for any changes in behavior that might occur over time the model could be easily altered to include outcome to motive dependencies while retaining the original assumptions of motives and rationality. Thus are outlined three models, each attempting to account for observed choice proportions and changes in choice proportions of game playing behavior. The research about to be reported attempts a simultaneous test of these, a test which could result in three possible outcomes. First, none of the models may account for the data beyond some chance level. Second, only one of the models may account for the data. And third, two or more models may account for i t . If the first outcome occurs, a sort of desperate post hoc rationalization is in order, attempting to explain why each model failed and why the results may have occurred as they did. But i f either the second or third outcome occurs an extensive analysis of the model's components is subsequently necessitated attempting to explain how the processes these models describe affect both one another and resulting behaviors. CHAPTER 3 EXPERIMENTAL METHOD The First Session The first session was undertaken primarily to obtain preference data on the utilities of those outcomes of the second and third session games so that the SEU model could be tested. Other preference data were also obtained under the assumption that i f the SEU model could be considered to account for subsequent game playing choices i t would be both legitimate and interesting to pursue how various components of the outcomes (own gain, joint gain and relative gain) combined to produce the subsequent overall utilities for each. Subjects Eighteen females (who formed nine dyads) ranging in age from 19 to 24, participated in this experiment, each recruited from an Introductory Psychology class on a volunteer basis. Upon recruitment, each Subject was told that the experiment concerned interpersonal decision making and that she would be required to participate one hour a week for three weeks coming to joint decisions with another female. She was also told that the results of these decisions would provide each Person with varying amounts of money, up to $1.50/week, which would be hers to keep. Upon arriving for the experiment, members of each dyad were asked i f they knew one another. Members of a l l dyads but one reported no prior acquaintance with one another? members of Dyad 7 reported knowing one another well for 20 about s i x years. Stimulus Materials T h i r t y - s i x 2Js:i x 3" cards were provided each Subject. On nine of these were printed one of the following statements: 1) Own gain maximum. 2) Own gain median. 3) Own gain minimum. 4) J o i n t gain maximum. 5) J o i n t gain median. 6) J o i n t gain minimum. 7) Own gain greater than other's. 8) Own gain equal to other's. 9) Own gain le s s than other's. On each of the remaining 27 cards was printed multiple statements: s p e c i f i c a l l y , one of the 27 possible combinations of three statements from the nine above, having one own gain statement (from 1-3 above), one j o i n t gain statement (from 4-6 above), and one r e l a t i v e gain statement (from 7-9 above). Procedure The rank ordering of the nine s i n g l e statements. Subjects mere f i r s t t o l d that momentarily they would each be choosing between a number of a l t e r n a t i v e outcomes. Each outcome would give e i t h e r one or both some amount of money; f o r example, an outcome could give person 1 5c and person 2 l C , or give both persons 3c eachj, or give person 1 0c and person 2 4c, etc. Subjects were then informed that though they would, never know the act u a l 21 monetary amount of each outcome they would be given a v e r b a l synopsis of some aspect of each. S p e c i f i c a l l y , Subjects would be t o l d whether t h e i r own gain was maximum, minimum or median (somewhere between maximum and minimum), whether t h e i r combined or j o i n t gain was maximum, minimum or median, or whether they were receiving more than, the same amount as or less than the other person ( r e l a t i v e gain). They were then given the nine s i n g l e statement cards and t o l d to rank order them i n terms of t h e i r preference for outcomes described by the statements occurring. Would they, f o r example, prefer an outcome which reported to maximize t h e i r combined or j o i n t gain but gave no information about t h e i r own gain or t h e i r r e l a t i v e gain, to an outcome which reported to give them some median amount of own gain but gave no information about t h e i r j o i n t gain or r e l a t i v e gain? As soon as both Subjects had rank ordered the nine si n g l e statement cards, they were c o l l e c t e d and t h e i r responses recorded. Preference for gambles (P.F.G.) task. Following the s i n g l e s t a t e -ment ranking task, Subjects were given, i n succession, three four-card sets with one own, j o i n t and r e l a t i v e gain statement printed on each (these were taken from the stack of 27). Each four-card set was composed of those four outcomes which would be displayed to Subjects i n one of Session Three's games. Upon being given a four-card s e t , Subjects were f i r s t i n s t r u c t e d to rank order the four cards i n terms of t h e i r d e s i r a b i l i t y as an outcome. These rankings were then recorded by the Experimenter, and the P.F.G. task, described e a r l i e r , to determine higher ordered metric representations of the u t i l i t i e s of these outcomes was immediately begun. In t h i s task a l l gambles were e i t h e r 50/59 chances between outcomes or 22 , ;sure things. ; i Subjects were informed that they would be paid the amount al l o c a t e d as t h e i r own gain i n the outcome they chose, plus the amount allocated to them i n the outcome the other person chose. Correspondingly, Subjects were also t o l d that the other person would be paid the amount allocated f o r her i n the outcome she chose, plus the amount a l l o c a t e d to her i n the Subject's chosen outcome. I f Subjects chose a gamble between two outcomes the Experimenter f l i p p e d a c o i n to determine which outcome the Subject would be credited with; i f Subjects chose a sure thing they would automatically be credited V7ith that outcome. Subjects made choices between gambles s i l e n t l y (by pointing) so that neither Subject would be influenced by the choice of the other. The Experimenter recorded t h e i r choices as made. The ranking of the 27 m u l t i p l e statements. Immediately a f t e r completing the P.F.G. task Subjects were given the 27 multiple statement cards and were asked to rank order them i n terms of t h e i r d e s i r a b i l i t y as outcomes. Aft e r completing t h e i r rankings the Experimenter recorded the r e s u l t s and informed the Subjects of how much money each had accrued by t h e i r choices i n the P.F.G. task (though he did not inform them of how much t h e i r own e f f o r t s had contributed to this t o t a l ) . The Experimenter, i n f a c t , a r b i t r a r i l y determined how much each vzas to be paid with the following r e s t r i c t i o n s : 1) Subjects received from 60c to 85c, and 2) no p a i r of Subjects received, sums more than 8c discrepant. R e s t r i c t i o n 1) was made as a compromise between giving subjects some f a i r return f o r t h e i r involvement and keeping enough funds to pay then f o r other sessions. 23 R e s t r i c t i o n 2) was made to minimize any systematic s h i f t i n motivation r e s u l t i n g from getting l e s s than the other. Subjects were asked to sign a r e c e i p t form and were asked i f they would consent to being credited with the amount earned and paid at the end of the t h i r d Session ( a l l agreed). The Experimenter then reminded them to come back at the same time the following week, not to speak to anyone about the experiment, and allowed them to leave. The Second Session In the Second Session Subjects played three games. These games served two primary functions: f i r s t , to f a m i l i a r i z e the Subjects with the game s i t u a t i o n and the 'rules'' of play, and with answering the questions asked of them before each t r i a l ; and second, to estimate the parameters of the RMP model. Subjects The Subjects i n the second Session were the same as those i n the f i r s t . A l l came exactly one week a f t e r p a r t i c i p a t i n g i n the f i r s t Session and a l l were paired with the same person with whom they had been previously paired. The Games The three games played i n th i s session are presented below. Verbal statements of payoffs were used instead of numerical statements f o r two reasons: 1) to help a l l e v i a t e whatever confusion might be encountered i n determining aspects of numerical payoffs such as j o i n t gain and r e l a t i v e 24 gain, 2) to minimize the confounding of the qualities of payoff attributes with the quantities of payoff attributes. OWN GAME JOINT GAK8 RELATIVE GAME As seen by Person I As seen by Person II (who chose between the rows) (who chose between the columns) X Y X Y A own gain maximum own gain median A own gain maximum own gain median 3 own gain median own gain minimum B own gain median own gain minimum X Y X Y A joint gain maximum joint gain median A joint gain maximum joint gain median B joint gain median joint gain minimum B joint gain median joint gain minimum A Y X Y A own gain equal to other's own gain less than other's A own gain equal to other's own gain greater than other's B own gain greater than other's own gain equal to other's B own gain less than other's own gain equal to other's The dominant solutions for the Own and Joint games were Row A and Column X, and for the Relative game were Row B and Column Y. If i t is assumed that utilities for outcome attributes were monotonie increasing with their objective value, then according to the SEU processes these ''solutions'1 should be played on every t r i a l . For each game the only rational solution to any motive was the one whose attributes were mentioned in the outcomes. For example, there were 25 no known j o i n t or r e l a t i v e gain solutions i n the own game so any A or X choices should r e s u l t from a Sabject being e i t h e r i n the own gain motive state or the Indifference motive state. For each game i t may be cal c u l a t e d that: and using such equations an estimate of each motive state may be made (see Results s e c t i o n f o r d e t a i l s ) . Apparatus The games were printed on 5'' x 5i: cards and superimposed over two game boards (one f o r each Subject). Each game board was a 6" x 10" x 3" metal box on which were mounted four outcome i n d i c a t o r l i g h t s labeled AX, AY, BX and BY (one i n each quadrant of the game card), two switches next to the rows f o r person 1 and next to the columns f o r person 2, and three l i g h t s i n a column on the far r i g h t hand side of the board labeled '"Estimate,'' "S e l e c t , " and "Reset." There was also an Experimenter's box 6" x 10" x 3" on which were mounted four l i g h t s labeled AX, AY, BX and BY fo r monitoring Subjects' responses, and three switches which activated the Subjects* "Estimate," 'Select," and i ;Reset : ! l i g h t s . The "Select" switch was wired i n s e r i e s with person l ' s row switches and person 2's column switches so that the "Select"' switch, one of the A or B switches and one of the X or Y switches a l l had to be activated before the Subjects' and Experimenter's outcome i n d i c a t o r l i g h t s came on. p(dominant a l t e r n a t i v e choice) = £ j p ( r e l a t i v e motive) + p ( i n d i f f ) p ( i r r e l e v a n t motive) 26 Procedure Subjects were seated facing one another at either end of a 5' x 6' table i n a well-lighted room 12' x 20' and were visually separated by a 5' x 3' black partition between them. While the games were i n progress the Experimenter sat at a 5' x 3' table about 8' to one side of the Subjects, visually separated from them by another 5' x 3' partition. Each Subject was f i r s t given a plastic-encased sheet of paper labeled QUESTIONS. On these were printed the following: 1) what do you think the chances are that the other person w i l l choose Column X (Row A) on the next t r i a l ? (Answer from 0 to 100 chances i n 100 of choosing this. Try to be as accurate as you possibly can.) 2) What Row (Column) do you plan to choose on the next t r i a l ? 3) Why? (Select the one most appropriate reason before each t r i a l . Your reason may change from t r i a l to t r i a l ; indicate this by appropriately changing your selection below.) OWN GAIN A) To try to get as much for myself as possible, regardless of what; the other person may get. B) To try to avoid getting the least for myself as possible, regardless of what the other person may get. JOINT GAIN C) To try to get as much jointly for both myself and the other person as possible, regardless of how much we individually may receive. D) To try to avoid getting the least jointly for both myself and the other person, regardless of how much we individually may receive. RELATIVE GAIN E) To try to get more than the other person, regardless of what I may receive for myself. F) To try to avoid getting less than the other person, regardless of what I may receive for myself. 27 OTHER G) To t r y to get the other person to change her choice on the next t r i a l . H) No p a r t i c u l a r reason. Mimeographed sheets containing three columns of blank spaces, and p e n c i l s were then given to the Subjects f o r recording t h e i r t r i a l - b y - t r i a l responses to these questions. The Experimenter began reading i n s t r u c t i o n s to the Subjects. They were t o l d that they would be making a number of choices i n three d i f f e r e n t s i t u a t i o n s , that both would receive money f o r these choices, but that how much each received would depend upon the choices both of them j o i n t l y made. They were also t o l d that although neither would know exactly how much each received f o r a choice, they would be t o l d something about the amount; i n one s i t u a t i o n they would be t o l d only about t h e i r own gain, i n another only about t h e i r j o i n t gain ( t h e i r ' s plus other's), and i n the t h i r d , only about t h e i r own gain r e l a t i v e to the other's. Subjects were further informed that i n each s i t u a t i o n they would make choices on a number of t r i a l s . Each t r i a l would consist of the f o l l o w i n g : f i r s t , the Estimate l i g h t would l i g h t up and each Subject would answer the three questions. Second, about 30 sec. l a t e r the Estimate l i g h t would go of f and the Select l i g h t would go on, at which time Subject 1 would s e l e c t a row and push i t s corresponding switch and Subject 2 would do the same f o r a column. When and only when both Subjects pushed a switch would they know the r e s u l t s of t h e i r j o i n t choice, indicated by the appropriate l i g h t i n one of the four quadrants of the outcome matrix. The Outcome l i g h t would remain l i g h t e d f o r about 10 sec. and Subjects should at t h i s 28 time read the statement next to t h i s l i g h t to determine whatever possible about the money each received. T h i r d , the Outcome l i g h t would go o f f and the Reset l i g h t would come on at which time Subjects would reset t h e i r row-column switches. This would end a t r i a l and another would immediately begin as soon as the Estimate l i g h t again came on. The t r i a l s would continue u n t i l the Experimenter instru c t e d them to stop. At t h i s time Subjects were extensively instructed on procedures f o r answering each question when the Estimate l i g h t came on. They were t o l d that to answer question 1 they should give t h e i r degree of personal b e l i e f that row A or column X would be selected by the other person on the next t r i a l . I f , f o r example, they were absolutely sure that the other person would choose t h i s they should put the number 100 i n the appropriate blank on the answer sheet. I f they were absolutely sure that the other person would not choose t h i s they should put a 0 i n the appropriate blank. And depending on t h e i r degree of c e r t a i n t y that row A or column X would be chosen they should put an appropriate number i n the blank. Subjects were t o l d not to choose merely f a v o r i t e numbers l i k e SO, 99, e t c . , unless they t r u l y r e f l e c t e d t h e i r degree of b e l i e f : they should try to be as accurate as p o s s i b l e . To answer question 2, Subjects were in s t r u c t e d merely to write down i n the appropriate blank on the answer sheet what they themselves were planning to choose on the next t r i a l , but that they were not obliged to choose t h i s , and i f they desired to change t h e i r mind i n the 15 seconds or so between answering and choosing, they could do so. To answer question 3 Subjects were t o l d to s e l e c t the one most appropriate statement of reason f o r choosing what they were about to choose, 29 and to write i t s corresponding l e t t e r i n the appropriate blank on the answer sheet. They were informed that t h e i r reason might change from t r i a l to t r i a l and that i f i t d i d to i n d i c a t e so by changing the selected statement. Each statement of reason was read aloud to the Subjects by the Experimenter, and explained to them. I t was noted that reasons A, C and E were what could be c a l l e d 'approach" reasons, and one should be selected i f a Subject was choosing i n order to attempt to "approach" or "get a t > ; a p a r t i c u l a r outcome. Reasons B, D and F were to be considered "avoidance reasons and to be selected i f a Subject was choosing i n order to "avoid" or "get away from" a p a r t i c u l a r outcome. Subjects were t o l d that as they selected from t r i a l to t r i a l t h e i r own choices might a f f e c t what the other would do on subsequent t r i a l s , and that i f e i t h e r was choosing to attempt a change i n the other's choice, reason G should be selected. F i n a l l y , Subjects were i n s t r u c t e d to use reason H i f on any t r i a l they could think of absolutely no reason f o r t h e i r choice or i f t h e i r reason included such things as "getting t i r e d of a p a r t i c u l a r switch" or 'wanting to hear what the other switch sounded l i k e ; M i n essence any reason having nothing to do with the s i t u a t i o n I t s e l f . They were warned not to use reason H as merely an easy way to avoid s e l e c t i n g among the others? to use i t only when they t r u l y f e l t i t was most appropriate. F i n a l l y they were t o l d not to t a l k at a l l during the experiment. Following the i n s t r u c t i o n s , E answered a l l questions and began the f i r s t game. Each game was run f o r twenty t r i a l s . To con t r o l f o r any order e f f e c t s , dyads 1, 4 and 7 played the games i n order J o i n t , Own, Relative; dyads 2, 5 and 8 i n order Own, Relative and J o i n t ; dyads 3, 30 6 and 9 i n order Relative, J o i n t and Own. Between games the Experimenter replaced the outcome matrix, c o l l e c t e d the answer sheets and gave out new ones. Subjects were t o l d at t h i s time that a l l monetary amounts i n the outcomes of the matrix now i n front of them were d i f f e r e n t than those i n the preceding outcome matrix and that t h e i r behavior i n the s i t u a t i o n now i n f ront of them should not i n any way be influenced by anything remembered from the other s i t u a t i o n s . A f t e r the three games were completed the Experimenter informed each Subject of the earnings accumulated. Again, these were, i n f a c t , a r b i t r a r i l y determined with the following r e s t r i c t i o n s : 1) a l l Subjects received from $1.20 to $1.40, 2) no members of a dyad were more than 10c discrepant, and 3) those members who, i n the f i r s t session, received more than the other, here received le s s than the other ( f o r r a t i o n a l e see Session Two's Procedure). Subjects were requested not to discuss the experiment with anyone and allowed to leave. The Third Session In the t h i r d Session three games were played as the primary test of a l l three models. Each game was composed of outcome statements f o r which higher ordered metric u t i l i t y data had been obtained i n the f i r s t Session. These data i n combination with t r i a l - b y - t r i a l p r o b a b i l i t y estimates would be s u f f i c i e n t to te s t the adequacy of the SEU model. From the response proportions i n any two of the games, the J o i n t , Own and Relative motive p r o b a b i l i t i e s could be estimated and a p r e d i c t i o n could be made as to the 31 proportion of A or X responses which should have resulted in the third game. This prediction, in combination with the data obtained in the trial-by-trial statement of Reasons for choices, formed tests of the R.M.P. model. The Markov model could, of course, be tested merely by noting trial-by-trial behaviors. Subjects The Subjects in the third session were the same as those in the first two. All dyads were composed of the same members as in the other sessions, appearing exactly one weak after the second one. Members of all dyads sat on the same side of the table as before. The Games The three games played in the session appeared as follows: As seen by Person I As seen by Person II (The JO-R Game) X Y X Y Own gain Own gain Own gain Own gain maximum median maximum median Joint gain Joint gain Joint gain Joint gain A maximum median A maximum median A Own gain Own gain A Own gain Own gain equal to less than equal to greater other's other's other's than other's E Own gain median Joint gain median Own gain greater than other's Own gain minimum Joint gain minimum Own gain equal to other's B Own gain median Joint gain median Own gain less than other's Own gain minimum Joint gain minimum Own gain equal to other's 32 As seen by P e r s o n I x y Own g a i n Own p a i n maximum minimum J o i n t g a i n J o i n t g a i n ••sxiraim m edian Own g a i n Own g a i n e q u a l t o e q u a l t o o t h e r ' s o t h e r ' s Own g a i n Ovn s a i n m a x i r a n mlnitfum J o i n t p a i n J o i n t p a i n median minirmm Or-.ni p a i n Own g a i n g r e a t e r e a u a l t o t h a n o t h e r ' s o t h e r ' s As s e e n by P e r s o n I Y Own prain Ovm g a i n m edian n i n i r u m J o i n t g a i n J o i n t g a i n naxinum median Own g a i n Own g a i n e q u a l t o l e s s t h a n o t h e r ' s o t h e r ' s Own Prain Chm g a i n ma iraum median J o i n t g a i n J o i n t p a i n median minimim Own g a i n Own g a i n g r e a t e r l e s s t h a n t h a n o t h e r ' s o t h e r ' s As s e e n by P e r s o n I I 7 Y Own g a i n Own g a i n naxiruim maximum J o i n t g a i n J o i n t p a i n naximur. median Ovm g a i n Own g a i n e q u a l t o e o u a l t o o t h e r ' s other'B Own R a i n *"Vn g a i n minimum minimum J o i n t p a i n J o i n t g a i n m edian n i n i n u m Own g a i n Ovm p a i n l e s s t h a n e o u a l t o o t h e r ' s o t h e r * s As s e e n by P e r s o n I I X y Own g a i n Own g a i n median maximum J o i n t p a i n J o i n t g a i n n a x i mur median Own g a i n Ovm g a i n e q u a l t o g r e a t e r o t h e r ' s t h a n o t h e r ' s Own g a i n Own g a i n Toininurn median J o i n t p a i n J o i n t p a i n median n i n i n u m Own g a i n Own g a i n l e s s t h a n e q u a l t o o t h e r ' s o t h e r ' s Ir. t h e JO-R pa^e row A pivA c o l u n n X were t h e r a t i o n a l s o l u t i o n s f o r n a x i r a i z i n g j o i n t and own p a i n s , w h i l e row ?> anr 1 column Y were t h e r a t i o n a l s o l u t i o n s f o r m a x i n i z i n g r e l a t i v e g a i n . I n the J-P. game, A and X were t h e s o l u t i o n s t o j o i n t p a i n , B and Y t o r e l a t i v e g a i n w i t h own g a i n h e l d 33 constant across rows and columns. And i n the J-OR game, A and X were the j o i n t gain solutions while B and Y were the solutions to both r e l a t i v e and own gains. These games were superimposed over the same game boards as those used i n Session Two. A l l other apparatus was also i d e n t i c a l to t h a t used i n the second Session. Procedure The t h i r d Session procedure was i d e n t i c a l with that of the second Session. A l l i n s t r u c t i o n s were repeated i n the same manner as before. I t was emphasized here> however, that each outcome had three statements about the monetary amount given therein, instead of one, and that the Subjects should note differences between outcomes f o r each of the own, j o i n t and r e l a t i v e gain statements to determine what, i f any, preferred outcomes existed f o r maximizing own, j o i n t and r e l a t i v e gains. Dyads 1-3 played the games i n order JO-R, J-R and J-OR; dyads 4-6 played i n order J-R, J-OR, JO-R: and dyads 7-9 i n order J-OR, JO-R, J-R. At the termination of this session, Subjects were debriefed, and a l l of t h e i r questions were answered. A l l were then paid $3.00 as t h e i r t o t a l earnings f o r the three sessions and allowed to leave. CHAPTER 4 RESULTS AND DISCUSSION Some General Results Table I presents the average number of joint choices selected, i n each of the three games of Session Two. Table I. Average number of choices i n each of Session Two's games Game Trials 1-10 AX AY BX BY Trials 11-20 AX AY BX BY Total AX AY BX BY Joint Own Relative 6.9 1.7 1.1 0.3 6.4 1.5 1.9 0.2 0.9 1.8 1.9 5.4 7.0 1.7 1.2 0.1 5.3 1.8 1.9 1.0 0.6 1.9 0.8 6.7 13.9 3.4 2.3 0.4 11.7 3.3 3.8 1.2 1.4 3.7 2.7 12.1 Recall that i n the Joint and Own games the A or X responses maximized the joint and own gain, respectively. From Table I i t may be determined that 33.4/40 = 84% of the Joint game choices and 30.6/40 = 76% of the Own game responses were A or X. In the Relative game B or Y responses maximized relative gain. From Table I i t may be seen that 30.8/40 = 77% of the Relative game choices were B or Y. Table II presents the average number of joint choices selected i n the games of Session Three. 35 Table I I . Average number of choices i n the games of Session Three Game T r i a l s 1-10 AX AY BX BY T r i a l s 11-20 AX AY BX BY To t a l AX AY BX BY JO-R J-R J-OR 6.1 1.4 1.3 1.1 3.9 1.6 2.7 1.8 2.1 1.4 2.9 3.6 6.0 1.3 1.6 1.1 4.0 0.8 2.4 2.8 2.8 1.3 2.4 3.5 12.1 2.7 2.9 2.2 7.9 2.4 5.1 4.6 4.9 2.7 5.3 7.1 Table I I shows that 29.8/40 = 74% of the JO-R game choices were A or X, 22.9/40 = 57% of the J-R game choices were A or X and 17.8/40 = 44% of the J-OR game's choices were A or X. An Analysis of Variance of Session Two's t o t a l A or X responses y i e l d s the r e s u l t s summarized i n Table I I I . Table I I I . Analysis of Variance summary table of the number of A or X choices i n the games of Session Two Source df SS MS F Between 8 116 Groups 2 15 7.5 S within groups 6 101 16.8 Within 18 3723 Order 2 35 ^17.5 Games 2 3151 1575.5 38.2* Residual 2 42 21 Error (within) 12 495 41.25 T o t a l 26 3839 *(p<.001) 36 From Table I I I i t may be seen that only the bwtween-games di f f e r e n c e was s i g n i f i c a n t . Verbal synopses of outcomes d i d , then, appear to have a noticeable e f f e c t on Subjects' choice behavior. I t also may be seen that between-Subject differences and game order apparently had no s i g n i f i c a n t e f f e c t upon choice proportions. An Analysis of Variance of Session Three's t o t a l A or X responses y i e l d s the r e s u l t s summarized i n Table IV. Table IV. Analysis of Variance summary table of the number of A of X choices i n the games of Session Three Source df SS MS F Between 8 1285 Groups 2 4 2.0 S w i t h i n groups 6 1281 213.5 8.31** Within 18 1169 Order 2 197 98.5 3.84* Games 2 650 325.0 12.66** Residual 2 14 7.0 Error (within) 12 308 25.7 T o t a l 26 2454 *p a .05 **p s .001 Table IV shows s i g n i f i c a n t game, order and between-Subject e f f e c t s . Thus, as i n Session Two, i t may be concluded that v e r b a l synopses of outcomes d i d 31 have an effect on choice behavior between games. The order effect was rather unexpected and requires further analysis. The average number of A or X responses in the first game played in Session Three was 25.8, in the second game i t was 19.9, and in the third game, 25.A. It appears that the order effect is due to a decrease in A or X choices given in the second game. No simple explanation for this dip is at hand, though in light of the fact that no such order effect occurred in Session Two or in any known game experiment with female subjects, i t is tempting to conclude that the effect was merely a statistical anomaly. Also of note was a significant difference between dyads over a l l games of Session Three. This difference did not appear in Session Two, but similar differences have been shown in numerous experiments mentioned in the Introduction. The between-dyad difference i s , therefore, assumed to be real. The Analysis of Variance presented in Table IV does not include a test for trends across the twenty trials within each game. However, from Table II, i t may be seen that in each game an approximately equal number of A or X responses occurred between trials 1-10 and trials 11-20. It may also be calculated that over a l l games 59% of the choices made in the first ten trials were A or X and 59% of the choices made in the second ten trials were A or X. On the basis of these observations alone i t seems reasonable to conclude that there was no noticeable trials effect within the games of Session Three. From these general results i t may be seen that the variance in choice proportions during Session Three was primarily a result of differences between games, between subjects and error. Each of the three models 38 previously o u t l i n e d must be Investigated as to t h e i r adequacy In accounting f o r the between-game and between-subject differences. These investigations s h a l l be presented separately and concluded with a comparison and synopsis. Results and Discussion of Tests f o r the Markov Process Model The Markov process was tested using Session Three r e s u l t s . Tables V - VII present the obtained response proportions of each dyad i n Session Three's games and the response proportions predicted by each dyad's estimated Markov process (predictions underneath a c t u a l ) . The predictions were derived by the method outlined i n Chapter 2. Table V. Actual response proportions and predicted response propor-tions (underneath actual) of each dyad f o r the JO--R game of Session Three. T r i a l s 1-10 T r i a l s 11-20 Total Dyad AX AY BX BY AX AY BX BY AX AY B X 3Y 1 .10 .10 .50 .30 .10 0 .50 .40 .10 .05 .50 .35 .10 .05 .52 .33 .11 .05 .47 .37 .10 .05 .50 .35 2 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 3 .40 0 .30 .30 .30 .30 .40 0 .35 .15 .35 .15 .35 .14 .35 .16 .34 .17 .34 .15 .34 .16 .34 .16 4 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 5 .50 .50 0 0 .60 .40 0 0 .55 .45 0 0 .55 .45 0 0 .57 .45 0 0 .56 .44 0 0 6 .60 .20 0 .20 .40 .10 .10 .40 .50 .15 .05 .30 .53 .15 .04 .28 .47 .16 .05 .32 .50 .16 .04 .30 7 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 8 .20 .40 .20 .20 .20 .30 .30 .20 .20 .35 .25 .20 .19 .37 .26 .19 .21 .32 .26 .21 .20 .34 .26 .20 9 .70 .10 .20 0 .80 .10 .10 0 .75 .10 .15 0 .78- .09 .13 0 .75 .10 .15 0 .76 .10 .14 0 .61 .14 .13 .11 .60 .13 .14 .10 .60 .14 .14 .10 X .61 .14 .14 .11 .60 .14 .13 .11 .60 .14 .14 .11 39 Table VI. Actual response proportions and predicted response proportions (underneath actual) of each dyad for the J-R game of Session Three. Trials 1-10 Trials 11-20 Total Dyad AX AY BX BY AX AY BX BY AX AY BX BY 1 0 .10 .60 .30 .10 0 .50 .40 .05 .05 .55 .35 .05 .05 .50 .33 .06 .06 .53 .35 .06 .06 .55 .34 2 1.0 0 0 0 11-0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 1.0 0 0 0 3 .30 .10 .30 .30 .50 0 0 .50 .40 .05 .15 .40 .37 .06 .20 .38 .43 .06 .08 .43 .40 .06 .14 .41 4 .70 .10 .10 .10 .60 .10 .30 0 .65 .10 .20 .05 .66 .10 .20 .04 .63 .10 .22 .05 .64 .10 .21 .04 5 .40 .50 0 .10 .10 .40 .40 .10 .25 .45 .20 .10 .28 .46 .17 .08 .21 .47 .21 .11 .24 .46 .19 .10 6 .10 .30 .40 .20 .40 .10 .30 .20 .25 .20 .35 .20 .21 .16 .43 .20 .26 .20 .33 .21 .24 .18 .38 .20 7 .70 .10 .10 .10 .50 .10 0 .40 .60 .10 .05 .25 .21 .13 .13 .53 .56 .11 .06 .27 .38 .12 .10 .40 8 .20 .10 .40 .30 .10 0 .40 .50 .15 .05 .40 .40 .14 .04 .43 .39 .16 .04 .37 .43 .15 .04 .40 .41 9 .10 .10 .60 .20 .30 0 .30 .40 .20 .05 .45 .30 .17 .05 .48 .30 .21 .05 .42 .31 .19 .05 .45 .30 V .39 .14 .28 .19 .40 .08 .24 .28 .39 .11 .26 .24 A .34 .12 .29 .25 .39 .12 .25 .24 .37 .12 .27 .24 40 Table VII. Actual response proportions and predicted response proportions (underneath actual) of each dyad f o r the J-OR game of Session Three. T r i a l s 1-10 T r i a l s 11-20 T o t a l Dyad AX AY BX BY AX AY BX BY . AX AY BX BY 1 0 .10 .20 .70 0 0 .20 .80 0 .05 .20 .75 0 .05 .16 .79 0 .05 .20 .75 0 .05 .18 .77 2 .50 .20 .20 .10 .60 .20 .10 .10 .55 .20 .15 .10 .53 .23 .14 .11 .61 .16 .15 .08 .56 .20 .14 .10 3 .40 0 .30 .30 .50 0 .30 .20 .45 0 .30 .25 .43 0 .34 .24 .45 0 .28 .27 .44 0 .31 .25 4 .10 .30 .10 .50 0 .20 .10 .70 .05 .25 .10 .60 .06 .25 .15 .54 .05 .25 .05 .65 .06 .25 .10 .59 5 .30 .20 .30 .20 .10 .10 .30 .50 .20 .15 .30 .35 .19 .13 .34 .34 .21 .17 .27 .35 .20 .15 .30 .35 6 .20 .10 .20 .50 .20 . 0 .30 .50 .20 .05 .25 .50 .17 .04 .25 .54 .21 .05 .26 .48 .19 .04 .26 .51 7 .10 .20 .40 .30 . .90 .10 0 0 .50 .15 .20 .15 .26 .17 .33 .24 .63 .15 .10 .13 .44 .16 .22 .18 8 .20 0 .50 .30 .10 .30 .60 0 .15 .15 .55 .15 .13 .13 .50 .24 .16 .16 .52 .16 .14 .15 .51 .20 9 .10 .20 .40 .30 .10 .30 .30 .30 .10 .25 .35 .30 .08 .24 .35 .33 .10 .26 .32 .32 .09 .25 .34 .32 .21 .14 .29 .36 .28 .13 .24 .34 .24 .14 .26 .35 X .20 .14 .26 .40 .27 .14 .24 .35 .24 .14 .25 .37 The greatest discrepancy i n p r e d i c t i n g o v e r a l l behavior f or each game occurred i n the J-R game where the average predicted proportion of AX responses was .02 = 2% low, and i n the J-OR game where the average predicted proportion of BY responses was .02 = 2% high. The greatest discrepancy i n pre d i c t i n g o v e r a l l behavior f o r each dyad occurred i n dyad seven (the two friends) where the average p r e d i c t i o n of AX responses was .093 = 9.3% lower than the proportion a c t u a l l y obtained. And the greatest discrepancy i n the p r e d i c t i o n of o v e r a l l behavior over time was during the f i r s t ten 41 t r i a l s when the average p r e d i c t i o n of AX responses was 2% high and of BY responses, 3.3% low. Thus, with the possible exception of dyad 7, i t seems reasonable to conclude that the Markov process can adequately account f o r the obtained behavior i n these three games. Dyad 7 presents a curious anomaly. The estimated Markov process parameters of t h i s dyad c l e a r l y f a i l to predict accurately both i t s o v e r a l l behavior and i t s time courses i n the J-R and J-OR games, p r e d i c t i n g o v e r a l l less AX responses than i n fact occurred. This f a i l u r e could r e f l e c t a v i o l a t i o n of either of the Markov process assumptions. F i r s t , i t may be that the members of t h i s dyad u t i l i z e d more information than what had occurred on the j u s t previous t r i a l i n making t h e i r choices. Second, the members may have changed t h e i r t r a n s i t i o n p r o b a b i l i t i e s from time to time. There i s i n s u f f i c i e n t information a v a i l a b l e to test these a l t e r n a t i v e s adequately, but a very crude analysis with the a v a i l a b l e data may be of some i n t e r e s t . In both the J-R and J-OR games, dyad 7 produced r e l a t i v e l y long runs of AX responses. A l l AX responses i n the J-D game were produced i n one run l a s t i n g from t r i a l s 10-19 i n c l u s i v e ; a l l those i n the J-OD game were produced i n one run l a s t i n g from t r i a l s 4-15 i n c l u s i v e . Thus, i n the J-D game there were ten AX responses, nine of which were followed by another AX, and i n the J-OD game twelve AX responses were made, eleven of which were followed by another AX. If members of t h i s dyad were basing t h e i r response propensities only on the j u s t previous t r i a l then p(AX/2AXs) would be p(AX/AX) • p(AX/AX). Therefore, i n the J-R game p(AX/2ASs>; should be 9/10 • 9/10 = .81, and i n the J-OR game i t should be 42 10/11 • 10/11 = .85. In the AX run of the J-R game there were nine pairs of two consecutive AX responses, eight of which were followed by another AX. Correspondingly, i n the J-OR game ten of the eleven AX pa i r s were followed by another AX. Thus, i n a c t u a l i t y , p(AX/2AXs), = .89 i n the J-R game and .91 i n the J-OR game. From t h i s i t may be concluded that there indeed was a s l i g h t l y greater propensity to follow two consecutive AX responses with another than to follow one AX response with another, though with such a small sample t h i s conclusion must remain highly tentative. An attempt to increase p r e d i c t i v e accuracy by basing predictions of response propensities on t r i a l s 1-10 using a t r a n s i t i o n matrix derived from these t r i a l s and basing predictions of response propensities on t r i a l s 11-20 using a matrix derived from these t r i a l s was unsuccessful. If members of t h i s dyad were a l t e r i n g t h e i r t r a n s i t i o n matrices i t was more l i k e l y a r e s u l t of some outcome • transition-matrix dependency than of any time or t r i a l s e f f e c t . S u f f i c e to say then, that despite t h i s dyad's deviance there i s i n s u f f i c i e n t evidence to suggest that their-behavior i n the J-R and J-OR games cannot be accounted f o r by some Markov process. Assuming that the Markov process can account rather w e l l f o r the observed behavior, the focus of inquiry i?.ust now s h i f t to the exploration of how t h i s process i s altered by the observed differences between games and persons. Table VIII presents the average s t a r t i n g propensities and t r a n s i t i o n p r o b a b i l i t i e s of each game i n Session Three. 43 Table VIII. Average t r a n s i t i o n matrices and s t a r t i n g propensities for each game of Session Three AX AY B7. BY AX AY BX BY AX AY BX BY AX .75 .14 .06 .05 AX .62 .13 .13 .12 AX .56 .09 .16 .19 AY .52 .09 .30 .09 AY .38 .19 .24 .19 AY .21 .12 .38 .29 BX .33 .12 .27 .23 BX .09 .09 .45 .36 ?•% .19 .13 .37 .30 BY .21 .21 .26 .32 BY .37 .10 .21 .32 BY .10 .19 .17 .53 AX AY BX BY AX AY BX 3Y AX AY BX F.Y .67 .22 .11 0 .33 0 .56 .11 0 .11 .56 .33 JO--R J- J--OR Assuming further that a cooperative response i n these games i s represented by those maximizing the j o i n t gain (A row and X column) and assuming that a competitive response i s represented by those maximizing the r e l a t i v e gain (B row and Y column), i t i s possible to rearrange the t r a n s i t i o n matrices i n t o the matrices presented i n Table IX. Table IX. The p r o b a b i l i t y of a person cooperating on a t r i a l following each of the four possible j o i n t responses i n the games of Session Three Weighted Person-Other JO-R J-R J-OR average Coop. - Coop. .84 .75 .69 .78 Coop• — Coop. .63 .55 .49 .55 Weighted average .80 .69 .60 Comp. - Ccaip. .65 .32 .41 .45 Comp. - Comp. .45 .53 .28 .35 Weighted average .50 .43 .33 44 From Table IX I t may be seen that the decrease i n the o v e r a l l proportion of cooperative responses between the JO-R and J-R games appears to be due to a decrease i n a person's propensity to cooperate following a cooperative-cooperative, cooperative-competitive, or competitive-cooperative j o i n t response. The decrease i n the o v e r a l l proportion of cooperative responses between the J-S and J-OR games appears to be due to a decrease i n a person's propensity to cooperate following a cooperative-cooperative, cooperative-competitive, or competitive-competitive j o i n t response. Following a person's cooperative response the e f f e c t s of differences i n games and of differences i n the other's behavior appear to be rather straightforward and addit i v e . In each game the p r o b a b i l i t y of a person cooperating on the t r i a l following a cooperative-cooperative j o i n t response i s about . 2 0 greater than on a t r i a l following a cooperative-competitive response. And as the maximization of Own gain i s s h i f t e d between the JO-R and J-OR games from a cooperative response to competitive one, an approximately equal drop i n a person's propensity to cooperate following both a cooperative-cooperative and a cooperative-competitive response appears to r e s u l t . But following a person's competitive response the e f f e c t s of d i f f e r -ences i n games appears to r e s u l t not only from an o v e r a l l main e f f e c t s i m i l a r to that between the games following a person's cooperative response, but also from a .strong i n t e r a c t i o n between the games and the other's response. In the J-R game the p r o b a b i l i t y of a person cooperating following a competitive-competitive response i s about . 2 1 greater than following a competitive-cooperative one. Yet, cur i o u s l y , the reverse seems true i n the 4 5 JO-R and J-OR games where the p r o b a b i l i t y of cooperating a f t e r a competitive-competitive response i s .20 and .13 l e s s , r e s p e c t i v e l y , than a f t e r a competitive-cooperative response. Assume f o r the moment that the greater the :'reward ,: of a choice the greater i t s l i k e l i h o o d of being chosen again on a subsequent t r i a l . In a l l three games the three aspects of the competitive-cooperative response payoff are greater than those of the competitive-competitive response payoff. I t seems reasonable to assume, therefore, that the '"reward" of a competitive-cooperative response should be greater f o r a person than the ' reward r of a competitive-competitive response and that a competitive-cooperative response should thus produce a greater propensity f o r a person to compete on the following t r i a l . This hypothesis i s not supported i n the JO-R and J-OR games, though a s i m i l a r hypothesis p r e d i c t i n g a greater propensity to cooperate following a cooperative-cooperative response than following a cooperative-competitive response i s supported i n a l l three games. A more b i z a r r e hypothesis must therefore be entertained. The JO-R and J-OR games d i f f e r from the J-R game i n that each has a dominant or c l e a r l y defined s o l u t i o n to the maximization of Own gain; whereas, i n the J-R game, no such s o l u t i o n e x i s t s . This suggests that the introduction of ''uncertainty 5 as to the means of assuring greatest personal gain may i t s e l f a l t e r cooperative response propensities following competitive-cooperative or competitive-competitive responses. TUit such a hypothesis must be seen as extremely tentative u n t i l further experimentation can r e p l i c a t e the r e s u l t and c l a r i f y the reason f o r i t . Let us now inve s t i g a t e how i n d i v i d u a l differences a f f e c t the 46 propensities to cooperate following any of the four po s s i b l e j o i n t responses. In terms of a Markov process persons can ei t h e r vary i n their t r a n s i t i o n p r o b a b i l i t i e s , or t h e i r s t a r t i n g p r o b a b i l i t i e s or both. I t seems appropriate to define i n d i v i d u a l differences i n terms of s t a r t i n g propensities and to determine how th i s difference r e l a t e s to i n d i v i d u a l t r a n s i t i o n p r o b a b i l i t i e s . But f i r s t I t i s necessary to show that f i r s t t r i a l responses are indeed rel a t e d to subsequent responses. On the f i r s t t r i a l of the J-R game f i v e dyads had one neraber choosing cooperatively and one member choosing competitively. Table X presents the number of subsequent cooperative responses produced by these persons on the remaining nineteen t r i a l s of th i s game. Table X. The number of cooperative responses given by members of f i v e dyads i n the J-R game who ei t h e r cooperated or competed on the f i r s t t r i a l Person Cooperating on f i r s t t r i a l Person Competing on f i r s t t r i a l 12 11 12 11 13 2 9 9 4 5 X = 11.8 X - 5.8 From Table X i t may be seen that what a person chose on the f i r s t t r i a l was, i n f a c t , r e l a t e d to the number of cooperative responses she subsequently made. Reneraber that members of each dyad were confronted with the same tx^enty outcomes i n t h i s game, so the difference i n t h e i r o v e r a l l l e v e l of 47 cooperation cannot be said to be due to any d i f f e r e n t i a l experiencing of outcomes. According to the Markov process t h e i r differences must, therefore, be due to one or more d i f f e r i n g propensities to cooperate following the four possible j o i n t responses. Table XI presents the average p r o b a b i l i t y of a cooperative response following these four possible j o i n t responses f o r those persons cooperating and those competing on the f i r s t t r i a l . Table XI. The p r o b a b i l i t y of persons who cooperated on t r i a l one and of persons who competed on t r i a l one of the J-R game cooperating on the t r i a l following each of four possible j o i n t responses Persons Cooperating Persons Competing Person-Other on t r i a l one on t r i a l one Coop.-Coop. 10/20 - .50 6/20 = .30 Coop.-Comp. 19/36 = .53 4/8 = .50 Comp.-Coop. 6/8 - .75 4/36 = .11 Comp.—Comp. 19/31 - .61 15/31 - .48 For convenience c a l l those persons cooperating on the f i r s t t r i a l , Cooperators, and t h e i r competitive counterparts, Competitors. Table XI; shows that, more than anything, Competitors seemed to produce fewer cooperative responses than Cooperators because of an increased propensity to choose competitively following a cooperative response by the other. This increased propensity was greatest following a competitive-cooperative response. Cccperatcrs appeared s l i g h t l y more i n c l i n e d to follow such a j o i n t response with a cooperative one of t h e i r own, almost as i f (to use 40 a homey expression) they f e l t ' guilty' 1 about either getting more than the other or about sacrificing joint gain. Competitors, i n contrast, were strongly inclined to follow a competitive-cooperative response with another competitive one of their own, as i f this outcome were somehow exceedingly satisfying to them. Results and Discussion of Tests for SEU Model First to be determined was to what extent Subjects' u t i l i t i e s for outcomes affected their subsequent behavior. Table XII presents the number of A or X responses of those persons in each game with A or X dominance, no dominance, or B or Y dominance. Table XII. First t r i a l and overall responses of persons with A or X dominance, no dominance, or B or Y dominance i n the games of Session Three. JO-R J-R J-OR A A A 1st or 1st or 1st or Dyad Dora. Choice X Dyad Dorn. Choice X Dyad Dom. Choice X 1 X X 12 1 X X 12 2 A A 15 2 A A 20 2 A A 20 3 X X 15 2 X X 20 2 X X 20 X=15.0 3 X X 14 7 X Y 13 1 - Y 4 4 A A 20 9 X X 13 5 - X 10 4 X X 20 =15.6 6 - B 5 5 X XT A 11 0 J - X 11 6 - Y 9 6 A A 13 4 -- A 15 9 — X 9 6 X X 11 4 - X 17 X=7.4 7 A A 20 6 - 9 1 B B 1 8 A A 11 7 - B 14 2 Y Y 14 8 X Y 9 3 ~ B 4 3 B ."-n 9 9 X X 18 8 -- X 11 L B B 6 15.3 9 - T> 5 4 Y X 3 3 - A 10 X-10.8 5 B B 7 5 - A 20 1 B R 2 7 B B 13 7 - X 20 3 3 B 9 7 Y X 14 9 - A 17 5 B 14 8 B B 6 X-16.7 5 Y X 9 8 Y Y 14 1 B B 3 6 Y V 12 9 B 3 7 X= 3.0 x-9.2 X=8.6 4* From Table XII It may be seen that, over a l l games, Subjects with an, A or X dominance chose an average of 15.4/20 A or X responses per game. Those with no dominance chose an average of 11.2/20 A or X responses per game. And those with a B or Y dominance chose an average of 8.4/20 A or X responses per game. Recall that the SEU model predicts, at best, that dominant choices should be chosen a l l of the time or at least a majority of the time. Those reporting an A or X dominance chose A or X 77% of the time, providing relatively good support for the SEU model. But those persons reporting a B or Y dominance chose B or Y only 58% of the time, providing very l i t t l e support for the SEU model. Next to be examined is i f , or to what extent, a person's probability estimates were altered as a result of the other's behavior. Consider an arbitrary sample of three consecutive responses by the other. In this sample, either 0, 1. 2 or 3 of the responses may be A or X. Table XIII presents a l l persoi.*' averaged probability estimate of whether the other w i l l choose A or X on the next t r i a l following each possible sample of three responses. Table XIII. Mean subjective probability estimates of other choosing A or X given by persons i n each game of Session Three following 0, 1, 2 or 3 A or X responses given by other i n the prior three t r i a l s . # of A or X responses given by other i n sample of 3 Game 0/3 1/3 2/3 3/3 JO-R .23 .54 .66 .90 J-R .35 .52 .63 .90 J«*0R .31 .47 .56 .82 Average .32 .50 .61 .89 50 From Table XIII i t may be seen that, i n general, persons d i d , i n f a c t , a l t e r t h e i r p r o b a b i l i t y estimates i n the l i g h t of the other's behavior. Individual differences i n these estimates were extreme, however: f o r example, p r o b a b i l i t y estimates of an A or X response following 0/3 of them, ranged from 0 to 100 with 6/42 being .75 or above. I t appeared that, though averaged p r o b a b i l i t y estimates seened c o n s i s t e n t l y a l t e r e d by the other's behavior, i n d i v i d u a l estimateswere f a r more sporadic. I t i s now necessary to determine whether these p r o b a b i l i t y estimates i n combination with a person's u t i l i t i e s can produce an accurate p r e d i c t i o n of t r i a l - b y - t r i a l choices. According to the model only those persons with a non-dominant s o l u t i o n to a game should a l t e r t h e i r choices as a r e s u l t of t h i s combination. So i t i s f i r s t necessary to determine a numerical representation of the u t i l i t i e s of those persons without a dominant a l t e r n a t i v e i n Session Three's games by r e f e r r i n g to the preference f o r gambles task data of Session One. Nine of the seventeen subjects with no domiRance i n one of these games.satisfied the t r a n s i t i v i t y requirement necessary for a computation of these numerical representations. Table XIV presents the nine higher ordered metric numerical representations (see Goode, 1961) of the u t i l i t i e s f o r each j o i n t response of Session Three's games. 51 Table XIV. The numerical representation of u t i l i t i e s f o r each of the four possible j o i n t responses f o r those persons i n each game of Session Three with no dominant s o l u t i o n and with usable higher ordered metric data J0--R J- •n J-OR Dyad-Rubject 7-2 9-1 3-2 7-1 8-1 9-1 5-2 6-1 9-2 Coop.-Coop. 6 6 6 6 6 6 9 6 9 Coop.-Comp. 0 4 0 0 0 0 0 0 0 Comp.-Coop. 4 9 5 5 5 c 6 5 7 Comp.-Comp. 1 0 2 2 2 2 4 2 4 Using the data from Table XIV i t i s possible to determine what may be c a l l e d a " c r i t i c a l subjective p r o b a b i l i t y " estimate of the other cooperating, above which a person should choose mora cooperatively and below which she should choose more competitively. That i s , knowing that: S.E.U. (cooperating) = U(coop.-coop.) x p(other cooperating) + U(coop.-comp.) x p(other competing) and S.E.U. (competing) * U(comp.-coop, x p (other cooperating) + U(comp.-comp. x p(other competing), and knowing U(coop.-coop.), U(coop.-comp.), U(comp.-coop.) and U(comp.-comp.), i t i s possible to determine the p(other cooperating) above which: S.E.U. (cooperating) > S.E.U. (competing) and below which S.E.U. (competing) > S.E.U. (cooperating) under the condition that U(coop.-coop.) > U(coop.-comp.); or to determine 52 the p(other cooperating) above which: S.E .U.(competing)>S.E.U.(cooperating) and below which S.E .U .(cooperating)>S.E .U .(competing) under the condition that U(comp.-coop.)>U(coon.-coop.). For example, from Table XIV i t can be seen that i n the JO-R game Subject two of dyad 7 had s i x points of u t i l i t y f o r the coop.-coop, j o i n t response, zero f o r the coop.-comp. j o i n t response, four f o r the comp.-coop. j o i n t response and one for the corap.-corap. one. Therefore: S.E . U .(cooperating) = 6 x p(other cooperating) + 0 x p(other competing), S.E .U. (competir.fr) = 4 x p(other cooperating) + 1 x p(other competing) and S.E .U.(cooperating)>S.E .U.(competing) when 6 x p + 0 x (l-p)>4 x p + 1 x (1-p) , or when 5p>3p + 1 3p>l p>l/3. Thus, according to the S.E .U. model every time t h i s Subject reports a p r o b a b i l i t y of the other cooperating greater than l/3:::=.33, she, h e r s e l f , should cooperate more often than compete. Correspondingly every time she reports a o r o b a b i l i t y of the other cooperating less than .33, she should compete more often than cooperate. Table XV presents the number of t r i a l s such predictions were confirmed as each person's subjective p r o b a b i l i t y fluctuated above and below the c r i t i c a l p r o b a b i l i t y . 53 Table XV. The number of confirmed and unconfirmed S .E .U. pre-dictions for each person of Session Three with an available numerical representation of their Outcome U t i l i t i e s J0-.1? J--P. J-OR Dyad-Subject • 7-2 9-1 3-2 7-1 8-1 9-1 5-2 6-1 9-2 Total Prediction confirmed 19 3 6 16 8 O o 10 14 14 98 Prediction unconfirmed i 17 14 4 12 12 10 6 f- 82 Assume, momentarily, that persons do not behave according to a S .E .U. model. Then one would expect that by chance the probability of confirming one of i t s predictions on any t r i a l would be given by the equation: p(prediction confirmed) = p(cooperating) x p[subjective p(other cooperating)>critical point] + p(competing) x p[subjective p(other cooperating)<critical point] . After determining this p(prediction confirmed) for each person i n Table XV and averaging them i t was found that p(prediction confirmed) by chance would be 0.53. In actuali ty , n(prediction confirmed) = 0.54. Thus, i t appears that, though a person's u t i l i t i e s for alternative choices do, to some extent, affect her overall proportion of choices and that the other's behavior does, to some extent, affect her reported subjective probabil i t ies , her t r i a l - b y - t r i a l behavior i s not based on the combination of u t i l i t i e s and subjective probabilities described by the S .E .U. models. 54 R e s u l t s and D i s c u s s i o n o f T e s t s f o r t h e R a t i o n a l M o t i v e P u r s u i t M o d e l Frora S u b j e c t s ' b e h a v i o r i n the 3ix ganes p l s y e d d u r i n g t h e e n t i r e e x p e r i m e n t , a t l e a s t f o u r p r o b a b i l i t y e s t i m a t e s o f b e i n p i n each o f t h e m o t i v e s t a t e s ( i c i n t , OTTO, r e l a t i v e and i n d i f f e r e n t ) may be o b t a i n e d . The f i r s t e s t i m a t e way be d e r i v e d from, t h e b e h a v i o r o b s e r v e d i n t h e games o f S e s s i o n Two. R e c a l l t h a t i n t h e J o i n t game t h e p r o b a b i l i t y o f a r-erson c h o o s i n g an A o r X a l t e r n a t i v e i s g i v e n by t h e f o r r i u l a ? !>(A o r X) = P ( j ) + + t p ( o ) + p ( r ) ] [ p ( j ) + v^-} + [p(o> + p ( r ) ] 2 [ r ( . i ) + r^f-) + • • • + [ p ( p ) + P ( r ) ] n [ P ( j ) + T ^ - ] w h i c h as n • «, approaches the. l i m i t P<A or X) = + (1) 1 [ o ( o ) + p ( r ) ] C o r r e s p o n d i n g l y s i n t h e Own game: p ( A o r X) = P ( P ) + : (2) 1 ~ tp ( . i ) + P ( r ) ] and i n t h e R e l a t i v e game: „,\ . AH. °r Y) = P U J + . (3) 1 -- [o(.i) + P ( o ) ] F u r t h e r m o r e f r o m t h e R..1?.P. p r o c e s s e s we know t h a t : p ( j ) + t)(o) + p ( r ) + p ( i ) = 1.00 r (4) and from t h e o b s e r v e d gana p l a y i n g b e h a v i o r we way e s t i m a t e t h a t p ( A o r ") i n J o i n t game = .84, p ( A o r X) i n Own game = .76, 55 i>(B or Y) i n Relative game = .77. Four equations (1-4) with four unknowns result and when solved they produce the motive state probability estimates given in Table XVI. Table; XVI. Probability estimates of beinp. i n each motive state derived from Subjects' behavior i n the games of Session Two Motive Joint Own Relative Indifferent .40 .22 .18 The second estimate nwty be derived by using the Indifferent estimate from Table XVI i n conjunction with any two of the games of Session Three. For examnle, reca l l that i n the JO-R game: , , . .» . , N , (indifferent) / C N p(.A or X) = p(joxnt) + p(own) + p-* ^ : (5) and i n the J-R game: p(A or X) = p ( j ) + P I " . (6) 1 - P(o) From Table II i t may be calculated that: p(A or X) i n the JO-R game = .74 (7) o(A or X) in the J-R game = .57 . (8) Substituting orobability estimates (7) and (8) and the indifference estimate from Table XVI into equations (4) - (6) the other motive state probabilities may be determined. Similarly , third and fourth estimates nay be derived fro'.", using the JO-R and J-OR games data or using the J-R and J-OR games 56 data. These estimates are given in Table XVII. Table XVII. Motive state probability estimates derived frora each set of two frames i n Session Three Derived from p(joint) p(ovjn) p(relative) p(indifferent) JO-R and J-R .25 .40 .17 .13 JO-R and J-03 .35 .30 • .17 .13 J-R and J-OR .35 .23 .24 .18 Maximum Likelihood .30 .32 .20 .18 From the motive probability estimates given in Tables XVI and XVII three predictions may be made of the proportion of A or 7. choices i n the games of Session Three. These predictions and the observed proportions are given i n Table XVIII. Table XVIII. The proportion of A or X choices predicted fror; three sources and observed in the games cf Session Three Predicted from: JO-R J-R J-OR Session Two .69 .61 .49 JO-R and J-P .34 JO-R and J-OR .63 J-R and J-OR .67 Maximum Likelihood .71 .57 .33 Observed .74 .57 .44 57 Table XVIII indicates that the predictions are only roughly equivalent to the observed proportions. The maximum likelihood predictions are closest, as would be expected. The other predictions, however, appear sufficiently deviant to warrant a brief inquiry into what extent these deviations resulted froia sampling errors or violations of at least one of the R.M.P. process assumptions. Recall that two important assumptions of the R.tf.P. process were: (1) a motive will be rationally pursued with p^l.OO when a person is in its state and a rational solution exists for i t , and (2) in any game the probability of being :'.n a particular motive state is independent of tri a l outcomes and constant over time. Let us examine these assumptions. Again, the constancy assumption, like its Markovian cousin, assumes that motive state probabilities, whether contingent on prior outcomes or not, renain constant over time. It thus seems reasonable to assume that these probabilities should, remain constant between games played in Session Three at least at the time of the first response of each. In the JO-R game 14/18 = 78% of the first responses were A or X, in the J-F. 61% were, and 33% were in the J-OR game. Assuining again that p(i) = .18 and is constant then, using equations (4) - (6) again, three related estimates of motive state probabilities may be made. These are given in Table XIX. Table XIX. Motive state probability estimates derived from the first t r i a l choices of Subjects in the games of Session Three Derived from p(joint) p(own) p(relative) p(indifferent) JO-R and J-R .25 .44 .23 .13 JO-R and J-OR .24 .45 .23 .18 J-R and J-OR .24 .46 .22 .18 58 Note that these estimates ere far less variable than those of Table XVII. Predictions of first t r i a l choice proportions in Session Three's games may, of course, be derived from these estimates. The predictions are given in Table XX. Table XX. Predictions of A or X choice proportions on the first t r i a l of Session Three games Predicted from: JO-R J-R J-OR JO-R and J-R .34 JO-R and J~0R .60 J-R and J-OR .79 Observed .78 .61 .33 Table XX shows the. predictions to be reasonably close, and the constancy assumptions must remain tenable. This implies, then, that the divergence of the similarly derived predictions from the observations presented in Table XVIII must have been due to a violation of (1) the rationality assumption, (2) the independence assumption, or both. According to the rationality assumption, in the JO-R game the following matrix is implied (call this Matrix A)? Choice cn trial n P(A or X) p(B or Y) j-.int 1.00 0.0 Motive own 1.00 0.0 on tr i a l n relative 0.0 1.00 indifferent .50 .50 59 Let p x - PI+ be the p r o b a b i l i t i e s of being i n the j o i n t , own, r e l a t i v e and i n d i f f e r e n t F o t i v e ^ s t a t e s , r e s p e c t i v e l y . Then according to the independence assumption the following matrix ( c a l l i t B) i s implied: Motive on t r i a l n j o i n t own r e l a t i v e i n d i f f e r e n t AX Pi P2 P3 Ptf Outcome of AY Pi P2 "3 P«t t r i a l n-1 BX Pi P2 P3 Pit BY Pi P2 P3 M u l t i p l y i n g the above two matrices A x B i t i s possible to predict that p(A or X) p(B or Y) AX Pi + P2 + ^ P3 Outcome of AY Pi + P2 £. P! t r i a l n-1 BX Pi + P2 + f- P3 BY °1 + P2 + 2k. 2 P3 Thus, according to the assumptions, i n the JO-R game the p(A or X) should be the same regardless of the previous outcome. S i m i l a r l y , within the J-R and J-OR games the p(A or X) should be the same regardless of the previous outcome. In f a c t , i t may be e a s i l y shown that regardless of the e n t r i e s i n matrix A (that i s , regardless of whether or not the r a t i o n a l i t y assumption i o v i o l a t e d ) the p(A or X) should be outcome independent. This p r e d i c t i o n may be tested i n each game by c o l l a p s i n g the matrices shown i n 60 Table VIII. These collapsed matrices are shown in Table XXI below. Table XXI. Collapsed transition matrices for the games of Session Three JO-R (A or X) (B or Y) J-R (A or X)(B or Y) J-OR (A or X) (B or Y) AX AY BX BY As can be seen from Table XXI the p(A or X) does not appear to be the same for a l l outcones in any of the games. This implies that either the motive probabilities are in some manner dependent upon the previous outcome, or that the probabilities of rationally pursuing motives fluctuate according to the previous outcome, or both. The probability of rationally pursuing a motive may depend upon the particular motive. But i t seems far more probable that i t is the motive state probabilities, and not the probabilities of rationally pursuing a motive, that are dependent upon the previous outcome. There are in-sufficient data available to determine 1) the motive • rationality dependency, 2) the outcome • rationality dependency, and 3) the outcome • motive dependency. But trial-by-trial Subject report data are available to determine any two of these, i f we assume a few things about the motive •»• motive report dependency and i f we assume something about 61 one of the three dependencies above. Without these assumptions a continuation of the discussion is impossible, but i f they are made and i f they appear at least intuitively reasonable, at least a few heuristic insights may result. For the sake of heuristics, then, let us begin by assuming that rationality is independent of prior outcomes, and attempt some analysis of whether or not the motive • rationality and the outcome »- motive dependencies exist, and i f so, to determine something about their nature. Subjects' answers to question three of the question sheet supposedly indicated their motive state from t r i a l to t r i a l . In the best of a l l possible worlds each motive report would indicate with perfect accuracy the "actual' motive state of the subject. That is to say, at best: p(motive 'mE[/report of motive "ra") = 1.00. If this is true, then the rationality assumption could be easily tested (and revised i f necessary) by pursuing the data to determine p(rational pursuit/motive report). One could also test the independence assumption (and revise i t i f necessary) merely by looking at p(motive report/outcome 0^) and p(rational pursuit/0^). Unfortunately, i t seems unlikely that persons do, in fact, report their motives xirith perfect accuracy. Therefore, any violations of the rationality and independence assumptions based on data from verbal reports could be accounted for by a failure to accurately report motives. To clarify the dilemma a diagram may be of use. Let 0^  ^ be two outcomes on tr i a l ,, M be trial n!s motive, EM be the report of motive M and n-1 n n n C be two choices on trial n. Let us speculate that? 62 (1) (2) > C 0 n-1 n n Relationships 3 and 5 may be computed from the data at hand. We wish tc determine r e l a t i o n 1 over a l l outcomes as a t e s t of the independence assumption, and r e l a t i o n 2 ns a te s t of the r a t i o n a l i t y assumption. Both of these may be determined i f r e l a t i o n 4 were known, but to determine r e l a t i o n 4 e i t h e r r e l a t i o n 1 or 2 i s needed. In order to transcend t h i s dilemma an assumption must be made about one of the three r e l a t i o n s , 1, 2 or 4. The assumed r e l a t i o n should i d e a l l y be robust so that the determination of the remaining r e l a t i o n s would not be d r a s t i c a l l y a l t e r e d i f the assumption were, i n f a c t , v i o l a t e d . And the assumed r e l a t i o n should be the one holding the l e a s t i n t e r e s t . C e r t a i n l y i n terms of the R .H.P. process s of l e a s t t h e o r e t i c a l i n t e r e s t f o r i t s e l f i s the p(motive/motive report). I t i s tempting to simply assume that t h i s p r o b a b i l i t y i s equal to 1.00 and to begin considering p(motive/outcome) and p(choice/motive). But f i r s t i t i s necessary to determine how these p r o b a b i l i t i e s are a l t e r e d i f the above assumption i s v i o l a t e d . I t may be e a s i l y shown that: * j=l J J I f pfcnotive reports/motive^) = 1.00 then a l i t t l e algebra w i l l show: p(chcice/motive.) = p(choice/motive repo r t . ) . x 63 Under t h i s assumption i n the JO-R game, for example, i t nay "be c a l c u l a t e d from the motive report data that: p(A or X/joint) = .88 p(A or X/own) = .70 p(A or X/ r e l a t i v e ) = .22 p(A or X/ i n d i f f e r e n t ) - .80. Assume now that p(motive reports/motive^) = .80.' then i n the JO-R game i t may be ca l c u l a t e d that p(A or X/joint) = .86 p(A or X/own) => .72 p(A or X/re l a t i v e ) = .32 p(A or X / i n d i f f e r e n t ) = .79. As may be seen above the discrepancy between assumptions (1.00 - 0.80 = 0.20) seemed to cause a r e l a t i v e l y small deviation i n the r e s u l t i n g r a t i o n a l pursuit p r o b a b i l i t y estimates, though the p(AX/relative) deviates more than might be hoped. Each set of four estimates retains the other's o r d i n a l properties, however, which at very least permits some discu s s i o n of inter-motive r a t i o n a l pursuit differences. Deviations from the assumption that p(motive reports/motive^) = 1.00 a f f e c t p(notive/outcome) estimates i n an equivalent manner to the p(choice/motive) estimates. Therefore i t seems acceptable to assume thn.t p(:notive report/motive) = 1.00 and to pursue a discussion of the p(motive/outcome) and p(choice/motive) dependencies, as long as the discussion of these two dependencies i s li m i t e d to t h e i r o r d i n a l properties. Again, the dependencies w i l l be analyzed from the reasons given 64 in Session Three. But recall that reasons were also given in Session Two during those games which contained a single payoff attribute in each outcome. Though not vital to any dependency analysis, i t is of interest to determine whether the nature of the payoff attribute given in the outcomes of a game affected the proportion of each reason given. Table XX2I shows the proportion of those 360 reasons given in each game of Session Two. (To review the eight reasons A-H see page 26.) Table XXII. The proportions of own, joint, relative, and other reasons given in the games of Session Two Own Joint Relative Other Game A and B C and D E and F G and E Joint .19 .68 ..04 .09 Own .58 .20 .09 .13 Relative .42 .25 .18 .15 Average .40 .38 .10 . .12 It may be seen fron XXII that the payoff attributes displayed in each game did appear to have an effect upon the proportion of reasons given. The greatest number of joint gain reasons occurred in the Joint game, the greatest number of own gain reasons occurred in the Own game and the greatest number of relative gain, reasons occurred in the Relative game. To the extent that reasons accurately reflect motives this finding replicates the result of Messick and T'c"lintock (1968) who found that the estimated proportions of being in the joint, own or relative gain motive 65 state were respectively greatest i n those Subjects playing games with j o i n t , own, or relative gain cumulative earnings displayed to them. In each game cf Session Three a total of 360 motive reports (here-after called a "reason") were given. Table XXIII presents the proportion of each reason given and the. proportion of times each was followed by an A or X and B cr Y choice. Table XXIII. The proportion of t r ia ls on which each reason (A—II) was used and pursued by an A or X, or B or Y choice i n the ganes of Session Three A or X B or Y P A or X B or Y P A or X B or Y P A .S3 .17 .28 A .50 .50 .29 A .19 .81 .25 B .29 .71 .09 B .34 .66 .11 B .14 .36 .16 C .91 .09 .42 C .37 .13 .36 C .80 .20 .30 D .62 .38 .06 T) .65 .35 .05 D .56 .44 .08 E .08 .92 .04 E .18 .82 .05 E .50 .50 .02 F .28 .72 .07 F .18 .82 .03 F .19 .81 .10 G .88 .12 .02 G .55 .45 .05 G .32 .18 .03 H .71 .29 .02 il .62 .38 .02 Ji .so .20 .01 JO-R J-R J-OR A number of things nay be noted about the data presented i n Table XXIII. F i r s t , in a l l three games there is markedly greater propensity to select raax-max own and joint gain reasons (A and C) than mini-max own and joint gain reasons (B and D). It appears that "Subjects i n an ovm or joint 66-motive state pursued the dominant s o l u t i o n , when i t existed, more to approach the OTTO or j o i n t gain naxiraun? than to avoid the own or j o i n t minimum. Second, i n a l l three ganes there i s a markedly greater propensity to s e l e c t the nini-max r e l a t i v e gain reason (F) than the max-max r e l a t i v e gain reason. Thus i t seems that Subjects i n the r e l a t i v e gain motive state pursued the dominant s o l u t i o n more to svoid getting l e s s than the other Subject than to attempt getting more than the other. This l a t t e r f i n d i n g supports a s i m i l a r r e s u l t reported by Messick and Thorngate (1967). In a l l three games reason G was followed by a cooperative choice more often than a competitive one. In these games a person's ovm, j o i n t and r e l a t i v e gains were always greater when the other cooperated than when she competed, so i t would be seemingly b e n e f i c i a l to induce the other to cooperate as nuch as pos s i b l e . I n t u i t i v e l y i t i s reasonable to suppose that a person would believe that the other could be induced to cooperate wore when he himself cooperated than when he competed. So the propensity to cooperate a f t e r declaring tho. desire to change the other's behavior (reason G) i s not s u r p r i s i n g on an i n t u i t i v e b a s i s . In each game reason G was used an average of 5% of the t i n e . Though t h i s reason hss no a c t i v e equivalent i n the R.U.P. model i t does suggest that future refinements should include some such t a c i t communication*' f a c t o r . Of tha 1.060 reasons selected over a l l subjects, t r i a l s and games, twenty were reeon Bf, the "indifference' reason. I t i s d i f f i c u l t to imagine ( e s p e c i a l l y i n the l i g h t of some informal observations) that Subjects were so enthralled i n these games as to eschew i n d i f f e r e n c e on a l l but about 27, of the t r i a l s . I t can only be speculated that perhaps 67 some tendency to avoid using the last reason, or some unfathomable social norm caused the Subjects' reluctance to give the Experimenter E. Regardless, i t should be noted that 14/29 of these reasons were followed by an A or X response which if? sufficiently close to the 10/20 predicted by the RMP Process's random pursuit of indifference assumption to consider i t s t i l l tenable. Table XXIV presents the proportion of times, over a l l games, each of the first six reasons was rationally pursued when a rational solution existed. Table XXIV. The proportion of times reasons A - F were rationally pursued when a rational solution existed Rational •^Rational A .82 .18 B .65 .35 C .87 .13 D .60 .40 E .SO .20 F .79 .21 Table XXIV shows the avoid-own-minimum reason (B) and the avoid-joint-minimum reason (D) were rationally pursued noticeably less than the approach-own-maximum (A) and approach-joint-maximum reason (C). However, the avoid-getting-less-than-other reason (F) was pursued rationally with a p p r o x i m a t e l y e q u a l p r o b a b i l i t y t o t h e a p p r o a c h - g e t t i n g - r a o r e - t h a n - o t h e r r e a s o n ( E ) . A t l e a s t two h y p o t h e s e s may be p o s i t e d t o e x p l a i n t h i s . F i r s t , s u b j e c t s s i m p l y nay have been l e s s r a t i o n a l when m o t i v a t e d t o a v o i d a n own o r j o i n t g a i n minimum t h a n when m o t i v a t e d t o a p p r o a c h t h e i r maximum. Second, S u b j e c t s nay have c o n f u s e d t h e a v o i d a n c e o f g e t t i n g t h e own o r j o i n t minimum w i t h the a v o i d a n c e of g e t t i n g l e s s t h a n t h e o t h e r . Note from T a b l e X X I I I t h a t i n t h e JO-V. game 29% o f t h e B r e a s o n s g i v e n were f o l l o w e d b y a r a t i o n a l c h o i c e and t h a t t h e o n l y minimum t o be a v o i d e d by an i r r a t i o n a l c h o i c e was 1 g e t t i n g l e s s t h a n t h e o t h e r " . I n t h e J-OR game 86% of t h e B r e a s o n s g i v e n were f o l l o w e d by a r a t i o n a l c h o i c e when the two mi n i r u i n s t o be a v o i d e d were ' g e t t i n g l e s s t h a n o t h e r and mininum own g a i n " . The n a t u r e o f t h i s d i f f e r e n c e i n d i c a t e s t h a t S u b j e c t s c o n f u s e d t h e a v o i d a n c e o f m i n i m i z i n g own g a i n w i t h t h e a v o i d a n c e o f g e t t i n g l e s s t h a n t h e o t h e r . I n the JO-R game 38% of t h e c h o i c e s f o l l o w i n g a D r e a s o n were i r r a t i o n a l , l e a d i n g o n l y t o t h e a v o i d a n c e o f m i n i m i z i n g r e l a t i v e g a i n . I n t h e J-OR game 44% o f the c h o i c e s f o l l o w i n g a D r e a s o n were r a t i o n a l where an i r r a t i o n a l c h o i c e , Egain l e d t o the a v o i d a n c e o f m i n i m i z i n g b o t h r e l a t i v e and own g a i n . The i n c r e a s e o f 6% i n i r r a t i o n a l l y p u r s u i n g a D r e a s o n from t h e JO-R to J-OP. games i n d i c a t e s t h a t S u b j e c t s may have had a s l i g h t t e ndency t o c o n f u s e t h e a v o i d a n c e o f m i n i m i z i n g j o i n t g a i n w i t h m i n i m i z i n g own g a i n , though t h e c o n f u s i o n , i f i t d i d e x i s t , was p r o b a b l y f a r l e s s t h a n t h a t between a v o i d i n g own and r e l a t i v e g a i n minimums. Most o f t h e d i f f e r e n c e s i n r a t i o n a l l y p u r s u i n g C and D r e a s o n s must t h e r e f o r e be ac c o u n t e d f o r by t h e o n l y r e m a i n i n g h y p o t h e s i s , namely t h a t S u b j e c t s do i n f a c t p u r s u e an ' a v o i d minimum" j o i n t g a i n m o t i v e s t a t e l e s s r a t i o n a l l y t h a n 69 an 'approach naximuro" one. Let us now examine any outcope »• notive dependencies. Table XXV shows the p r o b a b i l i t y of each reason being selected by a Subject following each of the four types of outcomes i n the ga^es of Session Three. Table XXV. The p r o b a b i l i t y of each reason being given following each type of outcotie i n the games of Session Three J0--R Person-Other A B C D F, F G H Coop.-Coop. .37 .07 .49 .03 .01 .02 0 .01 .61 Coop.-Comp. .14 .14 .39 .06 .02 .21 .04 0 .14 Conp.-Coop. .13 .08 .32 .17 .11 .11 .04 .04 .14 Corp.-Comp. .13 .20 .13 .10 .08 .15 .10 .05 .11 J-? Person-Other A B C D E F G I! Coop.-Coop. .31 .10 .53 0 .02 .01 .01 .02 .40 Coop.-Comp. .28 .16 .20 .11 .03 .09 .08 .05 .19 Comp.-Coop. .36 .09 .27 .05 .12 .09 .02 0 .19 Comp.-Comp. .17 .09 .22 .10 .05 .16 .17 .03 .22 J-OR Person-Other A E C D E F G 7.1 Coop.-Coop. .30 .07 .47 .06 0 .03 .02 0 .25 Coop.-Comp. .23 .13 .26 .10 C .15 .13 0 .20 Comp.-Coop. .27 .14 .30 .06 .03 .09 .10 .01 .20 Conp. - C O P P . .16 .27 .22 .10 .03 .10 .10 .02 .34 70 Table XXV shows that i n a l l three gar>es there was a marked increase i n the use of avoidance reasons (B, D, F) and a decrease i n the use of approach reasons (A, C, E) following a competitive choice by the other compared to t h e i r use following a cooperative choice by the other. R e c a l l that i t was a competitive other's choice which caused each payoff a t t r i b u t e ( j o i n t , own or r e l a t i v e gain) to be minimized f o r any given person's c h o i c e f and i t was a cooperative other's choice which caused each payoff a t t r i b u t e to be naxisized for any given person's choice. Thus the use of an ' approach or "avoidance' motive appears d i r e c t l y r e l a t e d to whether a person's p r i o r choice resulted i n the maximization or minimization of payoff a t t r i b u t e s i n those two possible outcomes which could have occurred given-his choice. It i s curious to note that an increase i n p a r t i c u l a r avoidance of minimum reasons would occur following outcomes i n which a t t r i b u t e s were not minimized. For example, neither the own gain nor j o i n t gain was minimized following a Coop.-Comp. outcome i n the JO-R game, yet there was a large increase i n the use of "avoid ovm minimum" and :'avoid j o i n t minimum'5 reasons (3 and D) over t h e i r use following a Coop.-Coop, outcome. Although some confusion of motives f a c t o r may account f o r such an increase, i t also may i n d i c a t e that Subjects were i n c l i n e d to evaluate an outcome more i n terns of how i t compared with the other one which could have occurred for a given a l t e r n a t i v e choice than i n terns of how i t compared with those outcomes of the choice not made. In other words, Subjects may be more i n c l i n e d to evaluate outcomes w i t h i n a l t e r n a t i v e s than outcomes between a l t e r n a t i v e s . Table XXV also shows that, regardless of what the other has chosen 71 on the l a s t outcome, the use of appr- uli or avoidance reasons on a p a r t i c u l a r t r i a l i s also dependent upon what the other has chosen on the l a s t outcome. In the JO-R game 17% of the reasons given following an outcome i n which a Subject cooperated concerned avoidance, while 41% of the reasons following an outcome i n which a subject competed were concerned with avoidance. In the J-P^ game the corresponding percentages were 19% and 30%, and i n the J-OR game they were 29% and 40%. No immediate explanation i s a v a i l a b l e f o r such ?n increase. But i n l i g h t of the hypothesis that Subjects tend to compare outcomes wit h i n an a l t e r n a t i v e choice nore than between a l t e r n a t i v e s i t could be speculated that Subjects came to a n t i c i p a t e that following t h e i r own competitive choice on a p a r t i c u l a r t r i a l a competitive choice of the other on the next t r i a l (one which w i l l minimize a l l a t t r i b u t e s of payoffs i n an al t e r n a t i v e ) was more c e r t a i n than i f they had cooperated. Being more certain, Subjects thus might have been more motivated to avoid i t and expressed such motivation i n t h e i r use of appropriate reasons. In general, Table XXV shows that the use of reason G was greatest following a competitive response by the other. Recall that reason G indicated a person's desire to t r y to induce the other to change her choice. Since a competitive choice of the other was always les s 'rewarding" to a person regardless of motive, the increased use of reason G following another's competitive choice i s not s u r p r i s i n g . Let us now consider the e f f e c t of outcomes upon the use of the combined own gain motives (A and B), j o i n t gain motives (C and D) and r e l a t i v e gain motives (E and F). Assume that a person i s i n one of the 72 two own, j o i n t , or r e l a t i v e gain motive states. We wish to determine to what extent remaining i n one of the two own, j o i n t or r e l a t i v e states i s dependent upon the j u s t previous outcome. Table XXVI presents average p r o b a b i l i t i e s over a l l games of staying i n one of the own, j o i n t or r e l a t i v e gain states following a cooperative or competitive other's choice. Table XXVI. The average p r o b a b i l i t y of a Subject continuing to use an own, j o i n t or r e l a t i v e gain reason on the t r i a l following a cooperative or competitive choice by the other Person Other's choice ,Own gain,. • reason /Another* reason Own gain reason Coop. Comp. .70 .52 .30 .48 Person Other's choice -.Joint gain, reason -Another.. P( ) r reason J o i n t gain reason Coop. Comp. .71 .52 .48 Person Other's choice -Relative gain.. p( ) reason /Another* P ( ) reason Relative gain reason Coop. Comp. .36 .37 .64 .63 It can be seen from Table XXVI thst following an own or j o i n t gain reason Subjects were more l i k e l y to give another own or j o i n t reason i f the other subject had cooperated than i f she had competed. One possible 73 explanation for this difference is that Subjects, in selecting an own or joint gain reason, established an "expectation" (to obtain the maximum own or joint gain or to avoid the minimum own or joint gain given their own choice) and i f this expectation was not fulfilled other reasons were selected. Curiously, the probability of a relative gain reason being followed by another was unaffected by the other's choice. This implies that the 'expectations1', given a relative pain reason, were somehow different fror those given an own or joint gain reason i f these expectations did, in fact, exist. However, tests for any "expectation" hypothesis are impossible witli the .'"ata at hand so any further speculation here seems unwarranted. So far this discussion of the P.M.P. modelhas focussed on between an-1 Tv'thin-gane differences. Let us now examine how between-Subject differences i?.ay he accounted for by theR.M.P. -modeL For purposes of comparison, only the data obtained from those five dyads considered in the Markov model discussion of individual differences will be considered. Recall that these five dyads were selected because each had a member choosing cooperatively and a member choosinp competitively on the first t r i a l of the J-S gane. On trials 2-20 of the JO-R game 64% of the five Cooperator'.^ choices were cooperative while 56% of the five Competitor's choices T?ere cooperative. In the J-R gam Cooperators gave 56% cooperative choices and Competitors, 31%° and in the J-OR. game they produced 52% and 29% coooerative choices, respectively. Assuming, again, that each group was in the indifferent motive state with p(i) = .18, a 74 maximum l i k e l i h o o d estimate of beinc* i n the other three motive states may be derived f o r the Cooperators an?1 f'.ompetitors i n a manner equivalent to the one describe.- previoualy (see Table XVIII). Table XXVII presents the maximum l i k e l i h o o d estimates f o r Cooperators and Competitors, along with the predicted an/*, observed proportion of cooperative responses i n each gane. Table XJ"II. Maximum l i k e l i h o o d motive state p r o b a b i l i t y estimates, derived predictions and observed prooortions of co-operative choices f o r Cooperators and Competitors i n the gores of Session Three Motive estimates- Ga^e Predicted Observed Cooperators JO-P, .61 .64 .1 o r i J-R .56 .56 .40 .12 .30 .IS J-OR .49 .52 Competitors JO-R .46 .56 •j o r i J-F .31 .31 .15 .22 .46 .13 J-0" .24 Table XXVII shows that Cooperators, as expected, appeared to hava a higher p r o b a b i l i t y of being i n the j o i n t gain state and a lower p r o b a b i l i t y of being i n the own or r e l a t i v e gain state than did Competitors. The predictions of cooperative choices derived from these estimates appear roughly concordant with those obtained but s u f f i c i e n t l y deviant to motivate the following rough analysis of th^ verbal reports. Table XXVIII 75 presents the reasons given by members of these d".<ids f o r making t h e i r p a r t i c u l a r cooperative or competitive choice on the f i r s t t r i a l . Table XXVIII, Reasons given on the f i r s t t r i a l of the J-R game by members of dyads who cooperated or competed on the f i r s t t r i a l Dyad F i r s t t r i a l choice 3 3 6 o u Q Cooperative A C A A C Competitive 1? A F E B With such, a s - i a l l nunber of observations Table XXVIII cannot providn enough data f o r any formal a n a l y s i s , but i t does seem to show a somewhat disproportionate use of r e l a t i v e gain and avoidance reasons by the Competitors i n comparison to the Cooperators. We have previously seen how Cooperators gave about twice as many cooperative responr.es on t r i a l s two through twenty of the J-R pane as Competitors (see Table >*). Tahle XXIX show? the average proportion c f times each reason was given by the f i v e Cooperators and f i v e Competitors on the same t r i a l s of t h i s game and the proportion of times each reason war, followed by a cooperative response. 76 TabL?. XXIX. The proportion of reasons used and the proportion followed by a cooperative choice for five Cooperators and for five Competitors averaged over trials 2-20 of al l the games of Session Three Cooperators Competitors reason p(reason) p(Coop. response/ reason) reason p(reason) p(Conp. response/ reason) A .24 .65 A .22 .22 B .16 .22 B .16 .03 c .31 .92 C .26 .60 D .07 c n * -« Ti .09 .32 E .02 .57 E .09 .00 F .12 .17 ji* .12 .22 C .05 .94 0 .06 .88 .02 .67 P .01 1.00 Table XXIX shows that Cooperators used own and joint gain reasons with approximately the same probability as Competitors and that Cooperators used relative gain reasons, especially reason E, somewhat less than Competitors. The greatest difference between Cooperators and Competitors appeared in their propensities to cooperate given an. own- joint or relative gain reason. On the average, 48% of the Cooperators' own gain reasons, 85% of their joint gain reasons and 23% of their relative gain reasons resulted in a cooperative choice. The corresponding percentages for Competitors were: own, 16%. joint, 66%? and relative, 12%. Thus, to the extent that 77 reasons reflected motives, the increased competitiveness of Competitors seemed due *;ore to an increased propensity to irrationally.pursue joint gain motives and competitively pursue own pain motives, than to a decreased tendency to actually select these motives. Table XXX shows Cooperator.1?' and Competitors' propensities to use various reasons following each of the four outcome types, averaged over al l three games of the Third Session. Table XXX. The propensities of Coonerators and Competitors to select various reasons following each outcome type averaged over a l l eames of Session Three Cooperators Competitors Pers.-Oth. <>.?n Joint Rela. Other Pers.-Oth. Ovm Joint Re la. Other Co op-Coop .51 .46 .03 .00 Coop-Coop .41 .41 .15 .03 Coop-Corcp .36 .35 .18 .09 Coor>~Corap .27 .38 .29 .06 Conp-Coop -.32 .52 .10 .06 Comp-Coop .37 .35 .24 .04 Comp-Conp .3? .28 .21 .12 Comp-Comp .37 .31 .18 .13 Perhaps the greatest difference between Cooperators and Competitors, as shown in Table XXX, is their propensity to select different reasons following a cooperative response by the other. Cooperators chose a joint gain reason an average of 48% of the tin's and a relative pain reason an average of 5% of the tine following a cooperative choice by the other. Competitors, on the averape, chose a joint pain reason 37% of the tine and a relative gain reason 20% of the time following a cooperative choice by the other. 78 Coonerators thu3 appear nore prone to establish what nay be loosely called a cooperative motivational set , whereas Competitors nprtear to adopt nore of an 'exploitative motivational set' following another's cooperative choice. CP.APTEP. FIVE S y n t h e s i s I n the p r e v i o u s t h r e e c h a p t e r s i t has been sbowr. t h a t t h e Markov model anpears t o a c c o u n t f o r t h e o b s e r v e d d a t a rrost a c c u r a t e l y , t h e R a t i o n a l * * o t i v e " u r s u i t model n e x t most a c c u r a t e l y , an-1 t h e S u b j e c t i v e E x p e c t e d U t i l i t y n o d e l l e a s t a c c u r a t e l y . The S.E.U. model was perhaps n o t g i v e n as ' f ? . i r a t e s t as t h e o t h e r s . I t s h o u l d be n o t e d t h a t of thr; t h r e e r.odels c o n s i d e r e d , t h e T.F.U. n o d e ! was t h e n o n t d i f f i c u l t t o t e s t s i n c e , u n l i k e t e s t s o f t h e o t h e r s w h i c h s i m p l y r e q u i r e d S u b j e c t s t o r a k e c h o i c e s i n v a r i o u s games, t h f S . F . l j . model f u r t h e r r e q u i r e d t h e use o f u t i l i t y and s u b j e c t i v e p r o b a b i l i t y e s t i m a t e s o b t a i n e d two weeks p r i o r t o t h e i r i n c o r p o r a t i o n i n p r e d i c t i n g b e h a v i o r . Y e t , more i m p o r t a n t t h a n the r e l a t i v e s u c c e s s of t h e s e models i n a c c o u n t i n g f o r t h e obperved b e h a v i o r , was t h e a b i l i t y o f each t o a c c o u n t f o r a t l e a s t sof-e of t h i s b e h a v i o r . Three i m p l i c a t i o n s r e s u l t . F i r s t , i t may have been t h a t p a r t i c u l a r p e r s o n s behaved i n c o m p l e t e a c c o r d w i t h one and o n l y one o f t h e s e models and t h a t i t s s u c c e s s i n p r e d i c t i n g any 'average " p e r s o n ' s b e h a v i o r was dependent upon how many o f i t s p e r s o n s happen t o have been s e l e c t e d f o r t h e e x p e r i m e n t . Second, i t nay have been t h a t a l l p e r s o n s a t c e r t a i n t i n e s a c t e d i n a c c o r d w i t h o r e and o n l y one o f t h e s e models and t h a t it«t s u c c e s s i n p r e d i c t i n g an "average 5' p e r s o n ' s b e h a v i o r depended upon the r e l a t i v e number o f p e r s o n s who were a c t i n g i n a c c o r d w i t h t h e model a t the t i m e t h e a v e r a g e wan t a k e n . T h i r d , a l l t h e models nay b e , i n s o r e manner, r e l a t e d , and ar>y d i f f e r e n c e i n p r e d i c t i v e s u c c e s s may r e s u l t f r o r ^ t h e n c t u r e o r e x t e n t of each model's 80 interdependency with the others. Ro doubt a l l three of these implications are to some extent correct, but the third implication appears most plausible with respect to the -'arkov, S .E .U. and models. Therefore, i t seem.s f i t t i n g to conclude this thesis with a discussion of the theoretical relationship between them. The R.'?.P. ?.nd S.E .U. models appear to d i f fer i n two rcalor aspects. F i r s t , they d i f f e r i n their c r i t e r i a for the selection of alternatives. The F . F . U . model assumes that given two alternatives, A and B ? i f S.F.u.(A)>P.E.U.(B) then A. w i l l be chosen over B, and i f S.E.U.(B)> S.E.U.(A) then P w i l l v e chosen over P. Th» T?.>?.p. model apparently* assumes that i f the minimum possible payoff of A is preater than the minimum possible payoff o f B, then A w i l l be chosen over F and vice versa, or that i f the iraximura payoff of / i s greater than the maximum, possible in then A w i l l be chosen over E and. vice versa. Second, they d i f f e r i n their treatment of a particular outcome's u t i l i t y ' or value' . The S.E.U. model assumes that the u t i l i t y of any outcome is a weighted sum of the u t i l i t i e s of i t s components or aspects. The P . . ¥ . P . model assumes that any apparent value of an outcome is some function (assumed here to be m.onotonically increasing) of that one payoff component or aspect relevant to the particular motive state i r which a nerson finds himself. In other words, for a particular outcome n 4 i n one of the Passion Three games: *""'essick and '-cClintock. 19*0, state that a motive w i l l lead to a choice i f one alternative i s dominant, or i n their words, 'well defined i n the relevant aspect. 81 U(0..) = a U ( j o i n t p.ain p a y o f f i n 0^) + bU(own g a i n p a y o f f i n 0^ ) + c l l ( r e l a t i v e g a i n p a y o f f i n C L ) , where a 5 h and c a r e c o n s t a n t s . I n t h e R.T-f.P. model i t may be i n t e r p r e t e d t h a t r " v a l u e " ( 0 ^ ) / j o i n t m o t i v e = a • " v a l u e " ( j o i n t p a i n n a y o f f i n 0^ ) , " v a l u e " (0^)/own m o t i v e = b • " v a l u e 1 " (OTTO g a i n p a y o f f i n 0^ ) , ( v a l u e ! : ( 0 ^ ) / r e l a t i v e m o t i v e = c - : v a l u e : ( r e l a t i v e p.ain n a y o f f i n 0^), v a l u e ' ( f . h ) / i n d i f f e r e n t m o t i v e = 0. The S.E.U. model,, by assuming t h a t u t i l i t i e s f o r outcomes r e m a i n c o n s t a n t o v e r t i m e ( o r a t e l e a s t v a r y i n d e p e n d e n t l y o^ i t ) , i m p l i e s e i t h e r t h a t t h e w e i g h t s o f each p a y o f f a s p e c t r e g a i n c o n s t a n t o v e r a l l m o t i v e s o r t h a t a p e r s o n ' s m o t i v e remains c o n s t a n t o v e r outcomes. The l a t t e r i m p l i c a t i o n has been shown f a l s e and t h e C o r n e r seems u n r e a s o n a b l e on i n t u i t i v e g r o u n d s . T h i s b e i n g t h e c a s e , a s y n t h e s i s o f t h e S.F.U. and ? . ? - . P . m o d e l s , j u s t i f i a b l e a t l e a s t f o r h e u r i s t i c p u r p o s e s , m i g h t be d e v i s e d as f o l l o w s . Assume t h a t * 1) ^n any t r i a l , l r ; t h e p r o b a b i l i t y of b e i n g i n m o t i v e s t a t e , m, i s e q u a l t o p ( n k ) = p(m/A:; k_ 1)p(AX,_ 1) + p ( n / A y t _ 1 ) P ( M k _ 1 ) + r f a / S X ^ p ^ X ^ j ) + p ( m / B Y k l ) p ( B Y k _ 1 ) and nOn/AXj^j), p f a / A V ^ ) , p f a / P X , ^ ) and p(m/BY k__j) a r e c o n s t a n t f o r a l l l<k<n. 2) The u t i l i t y o f a p a r t i c u l a r outcome 0^  i s dependent on m o t i v e s t a t e s , s p e c i f i c a l l y , 82 U ( ( l / j o i n t n o t i v e ) = U ( j o i n t ra.lv Dayoff i n 0^ ) iKO^/own m o t i v e ) = Tl(own g a i n p a y o f f i n 0 ) U f n ^ / r e l a t i v e m o t i v e ) •- U ( r e l a t i v e p a i n p a y o f f in. 0^) V(01/indifferent m o t i v e ) = 0, and t h a t g i v e n a motive., u t i l i t i e s have the sa!*e p r o p e r t i e s o f a d d i t i v i t y , c o n s t a n c y and i n v a r i a n c e d e s c r i b e d i n t h e o r i g i n a l S . E . U . p r o c e s s e a r l i e r . 3) O i v e n a m o t i v e s t a t e , m5 i n a game s i t u a t i o n l i k e t h a t used i n S e s s i o n T h r e e , and two a l t e r n a t i v e s A and ^ (SEU(A)/m.) = U ( A X / n ) p ( X ) + U ( A Y / B I ) P ( Y ) (SF.U(E)/m) = U(DX/m)p(X) + U(BY/n)p(Y). 4) F o r a g i v e n m o t i v e s t a t e , m, and t*ro a l t e r n a t i v e s A and B, A w i l l be ch o s e n more o f t e n t h a n E i f SEU(A/m.)> (SEU(I3/m) .• B w i l l be c h o s e n more o f t e n t h a n A i f SEU(B/ra)>REU(A/-:) .• and i f SEU(R/m) * S E U ( A / m ) , a n o t h e r sample fror.» t h e s e t o^ m o t i v e s w i l l be t a k e n u n t i l REU<A/mf)> o r < SEU(B/m'), o r u n t i l t h e i n d i f f e r e n c e m o t i v e s t a t e i s r e a c h e d , i n w h i c h c a s e A o r R w i l l be c h o s e n w i t h e q u a l p r o b a b i l i t y . 83 This hybrid model may be schematized i n the following flow diagram: s t a r t t r i a l s e l e c t r.otive state by ru l e of assumption 1) determine u t i l i t i e s of each out-come by ru l e of assumption 2) r determine SEU's of each a l t e r -native bv ru l e of assumption 3) i f SEU S are equal make choice by r u l e of assumption 4) determine subjective p r o b a b i l i t i e s by any means possible determine outcome Note that the hybrid has a peppering of assumptions from each of the Markov, P.M.P. and S.E.U. models. Assumption 1) i s l i k e the motive s e l e c t i o n assumption of the R.?I.P. model with a '-arkovian f l a v o r * assumptions 2), 3) and 4) are amalgums of those S.E.U. and model assumptions concerned with how to make a choice. One advantage to t h i s hybrid, i s i t s a b i l i t y to r a t i o n a l i z e the 84 apparent failure of subjects to combine subjective probability estimates with u t i l i t i e s in makinr choices. Pecall that the S.E.U. model dictated that an alternative, whose outcome u t i l i t i e s dominated other alternatives, should be selected exclusively regardless of any subjective probability  estimates. The «arae i s implied by the dictates of assumption 3), above. The S.E.U. model was tested using Subiects who, in Session One, produced a non-dominant ranking of the four outcomes in one of Session Three's games. For Subject 1 any one of the following outcome rankings would imply that no dominant alternative existed! for him? 1st choice: AX BX AY BY AX AY BX BY 2nd choice- P-X AX BY AY BY BX AY AX 3rd choice: BY AY BX AX BX BY AX AY 4th choice: AT BY AX BX AY AX BY BX There are numerous ways to obtain one th«se rankings given that the Subjects only consider payoff attributes of each outcome relevant to the particular motive state that they happen to be in at the time. For example, a Subject might be i n the indifferent motive state at the time of ranking,, i n which case the probability of selecting one of the rankings above would be 8/4! = 1/3. Regardless, the hybrid model dictates that on any t r i a l of a game a Subject would be in one and only one motive state. The games of Session Three were so constructed that (assuming u t i l i t i e s are monotone increasing with the magnitude of particular outcome attributes), given any motive state but indifference, the u t i l i t i e s of one alternative would dominate the other, with one exception. Of course, i n the J-P game there was no 85 dominant alternative for own gain. Instead the own gain was such that for a l l possible subjective probability estimates, S E u * A 8 0 S E U B * This being the case the hybrid model dictates that another selection of a motive would occur u n t i l one of those motives having u t i l i t y dominance for one alternative was selected or u n t i l the Subject entered indifference. Thus, in a l l of Session Three's games a choice was made as a result of being in a motive whose outcome u t i l i t i e s were dominant in one alternative or of being indifferent. In either case a selection could be made by assumption 4) without the "use" of subjective probability estimates. It i s possible to construct games with an arrangement of outcome attributes which would provide no dominant alternative for any motive. For example, i t i s reasonable to assume that the following game (as seen by person one) would have no dominant alternative for any of the motives. X Y own max own min A joint max joint min own « other own = other own median own median B joint median joint median own > other own < other Such a game would provide a better test of whether an S.E.U., minimax or max-max criterion was being employed as a basis for choice than the games used i n Session Three. There i s one interesting implication of the hybrid. Though u t i l i t i e s for outcome aspects given any particular motive are assumed 86 constant, the p r o b a b i l i t y of remaining i n that motive t r i a l a f t e r t r i a l i s allowed to vary as a function of a t r i a l ' s outcome. *:e have already seen that the p r o b a b i l i t y of s e l e c t i n g c e r t a i n motives does vary according to outcome.• f o r example, following another's cooperative response a person i s more l i k e l y to s e l e c t a j o i n t pain motive than following another's competitive response. This suggests th.^t u t i l i t i e s f o r s p e c i f i c outcomes would vary as a function of outcomes too. For example, i n the J-F. pame th-? u t i l i t y of the coop.-coop, outcome given a j o i n t gain motive i s greater than that of the conp.-coop, outcome. I f the p r o b a b i l i t y of being i n the j o i n t gain motive i s greater following a coop.-coop, outcome than, say, a coop.-comp. outcome, then the p r o b a b i l i t y of a Subject having greater u t i l i t y f o r the former i s also greater i f i t occurs than i f the l a t t e r occurs. A test of this i m p l i c a t i o n u t i l i z i n g some t r i a l by t r i a l estimates of outcome u t i l i t i e s would be i n t e r e s t i n g and b e n e f i c i a l . BIBLIOGRAPHY Ashby, T T. R. An I n t r o d u c t i o n t o C y b e r n e t i c s . New Y o r k : J o h n W i l e y and S o n s , 1963. B e c k e r , G. M., D e Groot, M . , and Marschuk, V. M e a s u r i n g u t i l i t y by a s i n g l e - r e s p o n s e s e q u e n t i a l method. Behav. S c i . , 1964, 9, 226-232. B e c k e r , G. M, f and ? J c C l i n t o c k , C. G. V a l u e : b e h a v i o r a l d e c i s i o n t h e o r y . Ann. Pev. o f P s y c h o l . , 1967, 13, 239-2S6. B u r k e , C. J . A p p l i c a t i o n s o f a l i n e a r model t o t w o - p e r s o n i n t e r a c t i o n s . I n S t u d i e s i n M a t h e m a t i c a l L e a r n i n g T h e o r y , C. V.. Bush and W. H s t e s , eds. S t a n f o r d : S t a n f o r d U n i v e r s i t y P r e s s , 1955, C h a p t e r 9. D a v i d s o n , D., Suppes, P., and S i e g e l , S. D e c i s i o n M a k i n g : An E x p e r i m e n t a l  A p p r oach . S t a n f o r d : S t a n f o r d U n i v e r s i t y P r e s s , 1957. D e u t s c h , >?. T r u s t , t r u s t w o r t h i n e s s , and t h e F s c a l e . J_. Abnorm. Soc. P s y c h o l . , 1960, 6 1 , 138-140. D e u t s c h , and K r a u s s , R. M. S t u d i e s o f i n t e r p e r s o n a l b a r g a i n i n g . J . C o n f l . R e s o l . , 1962, 5, 52-76. Edwards, w. Dynamic d e c i s i o n t h e o r y and p r o b a b i l i s t i c i n f o r m a t i o n p r o c e s s i n g . Run. F a c t o r s , 1962, 4, 59-73. G a l l o , ?. S., and M c C l i n t o c k , C. G. C o o p e r a t i v e and c o m p e t i t i v e b e h a v i o r i n m i x e d - m o t i v e games. J . C o n f l . R e s o l . , 1965, 9, 68-78. Goode, F. Two Methods f o r O b t a i n i n g I n t e r v a l S c a l e s from O r d e r e d M e t r i c S c a l e s (a n a p e r p r e s e n t e d a t •'idwestern P s y c h o l o g i c a l A s s o c i a t i o n , 1964). Knox, ^. Low p a y o f f s and m a r g i n a l comprehension* two p o s s i b l e c o n s t r a i n t s  upon b e h a v i o r i n the p r i s o n e r ' s d i l e r i n a . (Paper p r e s e n t e d a t W e s t e r n P s y c h o l o g i c a l A s s o c i a t i o n , San D i e g o , 1968). L oomis, J . L. Communication, t h e development of t r u s t and c o o p e r a t i v e b e h a v i o r . Hun. R e l a t . , 1959, 12, 305-315. L u c e , R. D., and. R a i f f a . H . Games and d e c i s i o n s . Few Y o r k : W i l e y and Sons I n c . , 1 9 5 7 . L u c e , R. D., and Suppes, P. P r e f e r e n c e , u t i l i t y , and s u b j e c t i v e p r o b a b i l i t y , I n Handbook o f M a t h e m a t i c a l P s y c h o l o g y . R. D. L u c e , R. P. Bush, and E. G a l a n t e r , eds. New Y o r k : W i l e y and Sons I n c . , 1965. 88 M c C l i n t o c k , C. G., U a r r l s o n , A. A., F t r a n d , S., and O a l l o . P. S. I n t e r n a t i o n a l i s m . . . i s o l a t i o n i s t : ' . , s t r a t e p v o f t h e o t h e r p l a y e r and two-person pane b e b . i v i o r . J. Abnom. Soc. P s y c h o l . , 1063, 67, 631-636. T'cClintock„ C. G., and " ' c ^ e e l , S. S o c i e t a l n e n ^ e r s h i p , s c o r e s t a t u s , and. pane b e h a v i o r . I n t e r n a t i o n a l J o u r n . of Psychol.,, 1966, 1, 263-279. ' ' c C l i n t o c V , C. G., and " rc*Jeel. S. reward and s c o r e f e e d b a c k as d e t e r m i n a n t s o f c o o p e r a t i v e and c o m p e t i t i v e pane b e h a v i o r . J . P e r s . Foe. P s y c h o l . , 1966, 4 r 606-613. ? f e s e l c k , T>. M . , an- • • ; c C l i n t o c l . 1 C. G. " o t i v a t i o n a l b a s e s of c h o i c e i n e x p e r i m e n t a l earres. J . F x p t l . Soc. ^ s y c h . o l . ( i n p r e s s ) . , ? e s s i c k , 0. M.. end T h o r n p a t e , T \ P. P e l a t i v e p a i n maximization, i n e x p e r i m e n t a l pam.es. J . ^ x n t l . ^ o c . P s y c h o l . , 1967, 2, 85-101. " i r n a s , J . S., S c o d e l , A.,, :'-.rlowe, ^.^ and 'awson, TT. Fome d e s c r i p t i v e a s p e c t s o f two p e r s o n n o n - z e r o sum panes. _J. P o n ^ l . ^ e s o l . , 1960, 4, 193-197. " p p o n o r t , The use and misus e o f pane t h e o r y . S c l . An., 1962, 108-118. R a p o p o r t 5 A., and Char-nab., A. P r i s o n e r ' s ^ilemn.a. Ann A r h o r • U n i v . " ' i c h i p a n " r e s s , 1965. P a p o p o r t . A., and Orwant, C. E x p e r i m e n t a l panes* a r e v i e w . Behav. f e i . , 1962. 1. 1 3 7 . Savape, L. J. . The F o u n d a t i o n s o f S t a t i s t i c a l I n f e r e n c e . :Tew YorV.' " i l e y and Tons, T n c . s 1962. F i o ^ e l , A method f o r o b t a i n i n g an o r d e r e d m e t r i c s c a l e , ^ s y c h o r . e t r i k a , 1956, 21, 207-216. S i e p e l , D e c i s i o n and C h o i c e 0 * e s s i c k , £>., and R r a y f i e l d , eds.) Vsv Vor 1-- '? c.-7raw- , Till rn.t 1964. Suppes, P., and A t k i n s o n , r . C. M a r k o v L e a r n i n p '-odels f o r " u l t i p e r s o n  I n t e r a c t i o n s . S t a n f o r d - S t a n f o r d U n i v e r s i t y P r e s s , 1960. T h o r n p a t e , ". ?.. The s y n t a c t i c , s e m a n t i c and c o s t l i m i t a t i o n s o f u s i n p game t h e o r y i n i n t e r n a t i o n a l r e l a t i o n s . U n p u b l i s h e d m a n u s c r i p t , 1968. T v e r s k y , A. A V . i t i v l t y A n a l y s i s o f T h o i c e F e h a v i o r - A T e s t o f U t i l i t y  T heory. Ann A r h o r - i * i c h . " ? t h . P s y c h o l . P r o g r . " e p t . , 1965. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0104348/manifest

Comment

Related Items