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Auctions in which Losers Set the Price

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  • Claudio Mezzetti

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  • Ilia Tsetlin

Abstract

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers’ bids. In particular, we show that the k-th price auction generates higher revenue than the second-price auction, for all k > 2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t + 1)-st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers’ bids. Finally, we compute bidding functions and revenue of the k-th price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions

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Bibliographic Info

Paper provided by Department of Economics, University of Leicester in its series Discussion Papers in Economics with number 06/8.

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Date of creation: Jul 2006
Date of revision: Mar 2007
Handle: RePEc:lec:leecon:06/8

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Related research

Keywords: Auctions; Second-Price Auction; English Auction; k-th Price Auction; Affiliated Values; Rationing; Robust Mechanism Design;

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  1. Jeremy Bulow & Paul Klemperer, 1999. "Prices and the Winner's Curse," Game Theory and Information 9904003, EconWPA.
  2. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," NajEcon Working Paper Reviews 666156000000000593, www.najecon.org.
  3. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  4. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-43, June.
  5. Parlour, Christine A. & Prasnikar, Vesna & Rajan, Uday, 2007. "Compensating for the winner's curse: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 60(2), pages 339-356, August.
  6. Kagel, John H & Harstad, Ronald M & Levin, Dan, 1987. "Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study," Econometrica, Econometric Society, vol. 55(6), pages 1275-1304, November.
  7. Vijay Krishna & John Morgan, 1994. "An Analysis of the War of Attrition and the All-Pay Auction," Game Theory and Information 9409002, EconWPA.
  8. Paul Klemperer, 2004. "Auctions: Theory and Practice," Economics Papers 2004-W09, Economics Group, Nuffield College, University of Oxford.
  9. Paul Klemperer, 2004. "Introduction to Auctions: Theory and Practice," Introductory Chapters, in: Auctions: Theory and Practice Princeton University Press.
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