Mezzetti, Claudio and Tsetlin, Ilia, 1970- (2007) On the lowest-winning-bid and the highest-losing-bid auctions. Working Paper. Coventry: University of Warwick, Department of Economics. (Warwick economic research papers.

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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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HF Commerce
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Auctions -- Mathematical models, Information asymmetry, Game theory, Mathematical models, Econometric models
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	30 November 2007
Number:	No.832
Number of Pages:	18
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Insead
Version or Related Resource:	Mezzetti, C. and Tsetlin, I. (2008). On the lowest-winning-bid and the highest-losing-bid auctions. Journal of Mathematical Economics, 44(9-10), pp. 1040-1048. http://wrap.warwick.ac.uk/id/eprint/29795
Related URLs:	Related item in WRAP
References:	Bikhchandani, S. and J. Riley (1991): Equilibria in Open Common Value Auctions, Journal of Economic Theory, 53, 101-130. Jackson, M. and I. Kremer (2004): The Relationship between the Allocation of Goods and a Seller's Revenue, Journal of Mathematical Economics, 40, 371-392. Jackson, M. and I. Kremer (2006): The Relevance of a Choice of Auction Format in a Competitive Environment, Review of Economic Studies, 73, 961-981. Kingman, J.F.C. (1978): Uses of Exchangeability, The Annals of Probability, 6, 183-197. Kremer, I. (2002): Information Aggregation in Common Value Auctions, Econometrica, 70, 1675-1682. McAdams, D. (2006): Uniqueness in Symmetric First-Price Auctions with Affliation, Journal of Economic Theory, in press, doi:10.1016/j.jet.2006.07.002 Mezzetti, C., A. Pekeµc, and I. Tsetlin (2007): Sequential vs. Single-Round Uniform-Price Auctions, Games and Economic Behavior, in press, doi:10.1016/j.geb.2007.05.002 Milgrom, P. (1981): Rational Expectations, Information Acquisition, and Competitive Bidding, Econometrica, 49, 921-943. Milgrom, P., and R. Weber (1982): A Theory of Auctions and Competitive Bidding, Econometrica, 50, 1089-1122. Milgrom, P.R., and R. Weber, (2000): A Theory of Auctions and Competitive Bidding, II in The Economic Theory of Auctions II, P. Klemperer, ed., Edward Elgar. Pesendorfer, W., and J. Swinkels (1997): The Loser's Curse and Information Aggregation in Common Value Auctions, Econometrica, 65, 1247-1281. Pesendorfer, W., and J. Swinkels (2000): Efficiency and Information Aggregation in Auctions, American Economic Review, 90, 3, 499-525. Robinson, M., (1985): Collusion and the Choice of Auction, Rand Journal of Economics, 16 (1), 141-145. Weber, R., (1983): Multi-Object Auctions, in R. Engelbrecht-Wiggans, M. Shubik and R. Stark (eds.), Auctions, Bidding and Contracting, New York University Press, New York.
URI:	http://wrap.warwick.ac.uk/id/eprint/1382

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