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Rank-Based Methods for the Analysis of Auctions

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Author Info
Ed Hopkins ()

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Abstract

A new method is proposed for the analysis of first price and all pay auctions, where bidding functions are written not as functions of values but as functions of the rank or quantile of the bidder’s value in the distribution from which it was drawn. This method gives new results in both symmetric and asymmetric cases with independent values. It is shown that under this new method if one bidder has a stochastically higher distribution of values then her bidding function in terms of rank will always be higher than her rival’s. This is a clearer result under weaker conditions than using standard methods. We also look at auctions where one bidder has more precise information than the other.

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Publisher Info
Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 173.

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Length: 14
Date of creation: 15 Oct 2007
Date of revision:
Handle: RePEc:edn:esedps:173

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Related research
Keywords: : first price auctions; all pay auctions; comparative statics; games of incomplete information; stochastic dominance; rank; quantile.;

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

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  1. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May. [Downloadable!] (restricted)
  2. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October. [Downloadable!] (restricted)
  3. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 439-54, July.
  4. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-42, February.
  5. Ed Hopkins & Tatiana Kornienko, 2007. "Cross and Double Cross: Comparative Statics in First Price and All Pay Auctions," Topics in Theoretical Economics, Berkeley Electronic Press, vol. 7(1), pages 1366-1366. [Downloadable!] (restricted)
  6. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April. [Downloadable!] (restricted)
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