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Wars of Attrition with Stochastic Competition

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  • Olivier Bos

Abstract

We extend the all-pay auctions analysis of Krishna and Morgan (1997) to a stochastic competition setting. In the war of attrition it does not directly follow from the first order condition that the bidding equilibrium strategy is a weighted average of the bidding equilibrium strategies that would be chosen for each number of bidders. This result contrasts with the characterization of the bidding equilibrium strategies in the first-price all-pay auction as well as the winner-pay auctions. Our findings are applicable to future works on contests and charity auctions.

Suggested Citation

  • Olivier Bos, 2010. "Wars of Attrition with Stochastic Competition," Working Paper Series in Economics 47, University of Cologne, Department of Economics.
    • Handle: RePEc:kls:series:0047
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    References listed on IDEAS

    as
    1. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    2. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, vol. 55(3), pages 633-646, May.
    3. Harstad, Ronald M. & Kagel, John H. & Levin, Dan, 1990. "Equilibrium bid functions for auctions with an uncertain number of bidders," Economics Letters, Elsevier, vol. 33(1), pages 35-40, May.
    4. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
    5. Harstad, Ronald M. & Pekec, Aleksandar Sasa & Tsetlin, Ilia, 2008. "Information aggregation in auctions with an unknown number of bidders," Games and Economic Behavior, Elsevier, vol. 62(2), pages 476-508, March.
    6. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    7. Jacob K. Goeree & Emiel Maasland & Sander Onderstal & John L. Turner, 2005. "How (Not) to Raise Money," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 897-926, August.
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    More about this item

    Keywords

    Wars of attrition; number of bidders;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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