UBC Theses and Dissertations

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UBC Theses and Dissertations

Analytical and empirical models of online auctions Ødegaard, Fredrik


This thesis provides a discussion on some analytical and empirical models of online auctions. The objective is to provide an alternative framework for analyzing online auctions, and to characterize the distribution of intermediate prices. Chapter 1 provides a mathematical formulation of the eBay auction format and background to the data used in the empirical analysis. Chapter 2 analyzes policies for optimally disposing inventory using online auctions. It is assumed a seller has a fixed number of items to sell using a sequence of, possibly overlapping, single-item auctions. The decision the seller must make is when to start each auction. The decision involves a trade-off between a holding cost for each period an item remains unsold, and a cannibalization effect among competing auctions. Consequently the seller must trade-off the expected marginal gain for the ongoing auctions with the expected marginal cost of the unreleased items by further deferring their release. The problem is formulated as a discrete time Markov Decision Problem. Conditions are derived to ensure that the optimal release policy is a control limit policy in the current price of the ongoing auctions. Chapter 2 focuses on the two item case which has sufficient complexity to raise challenging questions. An underlying assumption in Chapter 2 is that the auction dynamics can be captured by a set of transition probabilities. Chapter 3 shows with two fixed bidding strategies how the transition probabilities can be derived for a given auction format and bidder arrival process. The two specific bidding strategies analyzed are when bidders bid: 1) a minimal increment, and 2) their true valuation. Chapters 4 and 5 provides empirical analyzes of 4,000 eBay auctions conducted by Dell. Chapter 4 provides a statistical model where over discrete time periods, prices of online auctions follow a zero-inflated gamma distribution. Chapter 5 provides an analysis of the 44,000 bids placed in the auctions, based on bids following a gamma distribution. Both models presented in Chapters 4 and 5 are based on conditional probabilities given the price and elapsed time of an auction, and certain parameters of the competing auctions. Chapter 6 concludes the thesis with a discussion of the main results and possible extensions.

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