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

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Mezzetti, Claudio and Tsetlin, Ilia (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 (No.832).

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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

Official Date:

30 November 2007

Dates:

Date	Event
30 November 2007	Published

Number:

No.832

Number of Pages:

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Not Peer Reviewed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
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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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