Internet Auctions with Many Traders

We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogenous good, set reserve prices at their own independent second-price auctions. Each buyer has a private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between the sellers' auctions in a dynamic environment. We characterize a perfect Bayesian equilibrium for this decentralized trading mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform trading price. When the number of buyers and sellers is large but finite, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex-post efficiency is achieved. The buyers' strategies in this equilibrium are very simple and do not depend on their beliefs about the other buyers' valuations, or the number of buyers and sellers. They bid almost myopically. Their only `sophisticated' choice is where to bid when they are indifferent between several sellers.

[1]  Ángel Hernando Veciana.  Competition among auctioneers , 2001 .

[2]  Ennio Stacchetti,et al.  The English Auction with Differentiated Commodities , 2000, J. Econ. Theory.

[3]  Octavian Carare,et al.  Need for Speed: Demand Estimation Using Auction Data , 2001 .

[4]  Eddie Dekel,et al.  Rationalizable outcomes of large private-value first-price discrete auctions , 2003, Games Econ. Behav..

[5]  Michael Peters,et al.  A Competitive Distribution of Auctions , 1997 .

[6]  L. Shapley,et al.  College Admissions and the Stability of Marriage , 1962 .

[7]  V. Crawford,et al.  Job Matching, Coalition Formation, and Gross Substitutes , 1982 .

[8]  Michael Peters,et al.  Competition among Sellers Who Offer Auctions Instead of Prices , 1997 .

[9]  Vijay Krishna.  Asymmetric English auctions , 2003, J. Econ. Theory.

[10]  V. Smith.  An Experimental Study of Competitive Market Behavior , 1962, Journal of Political Economy.

[11]  Steven R. Williams,et al.  Bilateral trade with the sealed bid k-double auction: Existence and efficiency , 1989 .

[12]  Steven R. Williams,et al.  The Rate of Convergence to Efficiency in the Buyer's Bid Double Auction as the Market Becomes Large , 1989 .

[13]  Asher Wolinsky.  Dynamic Markets with Competitive Bidding , 1988 .

[14]  P. Herings,et al.  A globally and universally stable price adjustment process , 1997 .

[15]  Lawrence M. Ausubel,et al.  Ascending Auctions with Package Bidding , 2002 .

[16]  Ali Hortaçsu,et al.  Economic Insights from Internet Auctions , 2004 .

[17]  V. Krishna,et al.  Ecient Mechanism Design É , 1998 .

[18]  Steven R. Williams.  A characterization of efficient, bayesian incentive compatible mechanisms , 1999 .

[19]  Jeroen M. Swinkels,et al.  Efficiency and Information Aggregation in Auctions , 2000 .

[20]  Steven R. Williams,et al.  Convergence to Efficiency in a Simple Market with Incomplete Information , 1994 .

[21]  Thomas A. Gresik.  Ex ante incentive efficient trading mechanisms without the private valuation restriction , 1991 .

[22]  R. McAfee.  Mechanism Design by Competing Sellers , 1993 .

[23]  David Lucking-Reiley.  AUCTIONS ON THE INTERNET: WHAT'S BEING AUCTIONED, AND HOW?* , 2003 .

[24]  A. Roth,et al.  Last Minute Bidding and the Rules for Ending Second-Price Auctions: Theory and Evidence from a Natural Experiment on the Internet , 2000 .

[25]  Ali Hortaçsu,et al.  Winner's Curse, Reserve Prices and Endogenous Entry: Empirical Insights from Ebay Auctions , 2003 .

[26]  Eddie Dekel,et al.  Rationalizable Outcomes of Large Independent Private-Value First-Price Discrete Auctions , 2000 .

[27]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[28]  A. Roth,et al.  Two-sided matching , 1990 .

[29]  Ariel Rubinstein,et al.  Decentralized Trading, Strategic Behaviour and the Walrasian Outcome , 1990 .

[30]  Vijay Krishna,et al.  Efficient Mechanism Design , 1998 .

[31]  H. Leonard.  Elicitation of Honest Preferences for the Assignment of Individuals to Positions , 1983, Journal of Political Economy.

[32]  Jeroen M. Swinkels,et al.  Existence of Equilibrium in Single and Double Private Value Auctions , 2004 .

[33]  Robert H. Wilson.  Incentive Efficiency of Double Auctions , 1985 .