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Internet Auctions with Many Traders

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  • Peters, Michael
  • Severinov, Sergei

Abstract

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.

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Bibliographic Info

Paper provided by Vancouver School of Economics in its series Microeconomics.ca working papers with number peters-05-03-30-03-06-03.

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Length: 47 pages
Date of creation: 30 Mar 2005
Date of revision: 23 Jan 2006
Handle: RePEc:ubc:pmicro:peters-05-03-30-03-06-03

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Web page: http://www.economics.ubc.ca/

Related research

Keywords: internet auctions; double auction; Bayesian equilibrium;

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References

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  1. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
  2. Michael Peters & Sergei Severinov, 1995. "Competition Among Sellers who offer Auctions Instead of Prices," Working Papers peters-95-02, University of Toronto, Department of Economics.
  3. Satterthwaite, Mark A. & Williams, Steven R., 1989. "Bilateral trade with the sealed bid k-double auction: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 48(1), pages 107-133, June.
  4. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  5. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  6. Wilson, Robert B, 1985. "Incentive Efficiency of Double Auctions," Econometrica, Econometric Society, vol. 53(5), pages 1101-15, September.
  7. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
  8. Satterthwaite, Mark A & Williams, Steven R, 1989. "The Rate of Convergence to Efficiency in the Buyer's Bid Double Auction as the Market Becomes Large," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 477-98, October.
  9. Rustichini, Aldo & Satterthwaite, Mark A & Williams, Steven R, 1994. "Convergence to Efficiency in a Simple Market with Incomplete Information," Econometrica, Econometric Society, vol. 62(5), pages 1041-63, September.
  10. Michael Peters, 1995. "A Competitive Distribution of Auctions," Working Papers peters-95-03, University of Toronto, Department of Economics.
  11. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
  12. Vernon L. Smith, 1962. "An Experimental Study of Competitive Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 70, pages 111.
  13. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
  14. Rubinstein, Ariel & Wolinsky, Asher, 1990. "Decentralized Trading, Strategic Behaviour and the Walrasian Outcome," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 63-78, January.
  15. Ángel Hernando Veciana, 2001. "Competition Among Auctioneers," Working Papers. Serie AD 2001-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  16. Wolinsky, Asher, 1988. "Dynamic Markets with Competitive Bidding," Review of Economic Studies, Wiley Blackwell, vol. 55(1), pages 71-84, January.
  17. Gresik, Thomas A., 1991. "Ex ante incentive efficient trading mechanisms without the private valuation restriction," Journal of Economic Theory, Elsevier, vol. 55(1), pages 41-63, October.
  18. Krishna, Vijay, 2003. "Asymmetric English auctions," Journal of Economic Theory, Elsevier, vol. 112(2), pages 261-288, October.
  19. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-79, June.
  20. Alvin E. Roth & Axel Ockenfels, 2000. "Last Minute Bidding and the Rules for Ending Second-Price Auctions: Theory and Evidence from a Natural Experiment on the Internet," NBER Working Papers 7729, National Bureau of Economic Research, Inc.
  21. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
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