Mezzetti, Claudio and Tsetlin, Ilia, 1970-. (2008) On the lowest-winning-bid and the highest-losing-bid auctions. Journal of Mathematical Economics, Vol.44 (No.9-10). pp. 1040-1048. ISSN 0304-4068

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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. (C) 2007 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
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, Econometric models
Journal or Publication Title:	Journal of Mathematical Economics
Publisher:	Elsevier
ISSN:	0304-4068
Date:	September 2008
Volume:	Vol.44
Number:	No.9-10
Number of Pages:	9
Page Range:	pp. 1040-1048
Identification Number:	10.1016/j.jmateco.2007.12.001
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Version or Related Resource:	Mezetti, C. and Tsetlin, I. (2007). On the lowest-winning-bid and the highest-losing-bid auctions. [Coventry] : University of Warwick, Economics Department. (Warwick economic research papers, no.832). http://wrap.warwick.ac.uk/id/eprint/1382
Related URLs:	Related item in WRAP
References:	Bikhchandani, S., Riley, J., 1991. Equilibria in open common value auctions. Journal of Economic Theory 53, 101–130. Jackson, M., Kremer, I., 2004. The relationship between the allocation of goods and a seller’s revenue. Journal of Mathematical Economics 40, 371–392. Jackson, M., Kremer, I., 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., 2007. Uniqueness in symmetric first-price auctions with affiliation. Journal of Economic Theory 136, 144–166. Mezzetti, C., Pekeˇc, A., Tsetlin, I., 2008 Sequential vs. single-round uniform-price auctions. Games and Economic Behavior, 62, 591–609. Milgrom, P., 1981. Rational expectations, information acquisition, and competitive bidding. Econometrica 49, 921–943. Milgrom, P., Weber, R., 1982. A theory of auctions and competitive bidding. Econometrica 50, 1089–1122. Milgrom, P.R., Weber, R., 2000. A theory of auctions and competitive bidding, II. In: Klemperer, P. (Ed.), The Economic Theory of Auctions II. Edward Elgar. Pesendorfer, W., Swinkels, J., 1997. The loser’s curse and information aggregation in common value auctions. Econometrica 65, 1247–1281. Pesendorfer, W., Swinkels, J., 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: Engelbrecht-Wiggans, R., Shubik, M., Stark, R. (Eds.), Auctions, Bidding and Contracting. University Press, New York.
URI:	http://wrap.warwick.ac.uk/id/eprint/29795

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