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On the lowest-winning-bid and the highest-losing-bid auctions

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  • Mezzetti, Claudio
  • Tsetlin, Ilia

Abstract

Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for sale and n bidders with unit demand, and prove that it converges to the bidding function of the highest-losing-bid auction if and only if the number of losers n-k gets large. When the number of losers grows large, the bidding functions converge at a linear rate and the prices in the two auctions converge in probability to the expected value of an object to the marginal winner.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 9-10 (September)
Pages: 1040-1048

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Handle: RePEc:eee:mateco:v:44:y:2008:i:9-10:p:1040-1048

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Web page: http://www.elsevier.com/locate/jmateco

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  1. Bikhchandani, Sushil & Riley, John G., 1991. "Equilibria in open common value auctions," Journal of Economic Theory, Elsevier, vol. 53(1), pages 101-130, February.
  2. Wolfgang Pesendorfer & Jeroen M. Swinkels, 1996. "Efficiency and Information Aggregation in Auctions," Discussion Papers 1168, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. McAdams, David, 2007. "Uniqueness in symmetric first-price auctions with affiliation," Journal of Economic Theory, Elsevier, vol. 136(1), pages 144-166, September.
  4. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Ilan Kremer, 2002. "Information Aggregation in Common Value Auctions," Econometrica, Econometric Society, vol. 70(4), pages 1675-1682, July.
  6. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-43, June.
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Cited by:
  1. Mezzetti, Claudio & Pekec, Aleksandar Sasa & Tsetlin, Ilia, 2008. "Sequential vs. single-round uniform-price auctions," Games and Economic Behavior, Elsevier, vol. 62(2), pages 591-609, March.
  2. Han Hong & Harry J. Paarsch & Pai Xu, 2010. "On the Asymptotic Distribution of the Transaction Price in a Clock Model of a Multi-Unit, Oral, Ascending-Price Auction within the Common-Value Paradigm," Carlo Alberto Notebooks 186, Collegio Carlo Alberto.

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