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Rank-Based Methods for the Analysis of Auctions

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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.

Suggested Citation

  • Ed Hopkins, 2007. "Rank-Based Methods for the Analysis of Auctions," ESE Discussion Papers 173, Edinburgh School of Economics, University of Edinburgh.
  • Handle: RePEc:edn:esedps:173
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    References listed on IDEAS

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    1. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    2. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    3. 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.
    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 125-142, February.
    5. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    6. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
    7. Ed Hopkins & Tatiana Kornienko, 2007. "Cross and Double Cross: Comparative Statics in First Price Auctions," Levine's Bibliography 321307000000000831, UCLA Department of Economics.
    8. Hopkins Ed & Kornienko Tatiana, 2007. "Cross and Double Cross: Comparative Statics in First Price and All Pay Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-25, May.
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    Cited by:

    1. Kirkegaard, René, 2014. "Ranking asymmetric auctions: Filling the gap between a distributional shift and stretch," Games and Economic Behavior, Elsevier, vol. 85(C), pages 60-69.
    2. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
    3. Mares, Vlad & Swinkels, Jeroen M., 2014. "On the analysis of asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 152(C), pages 1-40.
    4. Kirkegaard, René, 2012. "Favoritism in asymmetric contests: Head starts and handicaps," Games and Economic Behavior, Elsevier, vol. 76(1), pages 226-248.

    More about this item

    Keywords

    first price auctions; all pay auctions; comparative statics; games of incomplete information; stochastic dominance; rank; quantile;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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