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Wars of attrition and all-pay auctions with stochastic competition


  • Bos, Olivier


We extend the war of attrition and all-pay auction analysis of Krishna and Morgan (1997) to a stochastic competition setting. We determine the existence of equilibrium bidding strategies and discuss the potential shape of these strategies. Results for the war of attrition contrast with the characterization of the bidding equilibrium strategies in the first-price all-pay auction as well as the winner-pay auctions. Furthermore we investigate the expected revenue comparisons among the war of attrition, the all-pay auction and the winner-pay auctions and discuss the linkage principle as well. Our findings are applicable to future works on contests and charity auctions.

Suggested Citation

  • Bos, Olivier, 2012. "Wars of attrition and all-pay auctions with stochastic competition," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 83-91.
  • Handle: RePEc:eee:mateco:v:48:y:2012:i:2:p:83-91 DOI: 10.1016/j.jmateco.2011.12.002

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    References listed on IDEAS

    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. Aleksandar Saša Pekev{c} & Ilia Tsetlin, 2008. "Revenue Ranking of Discriminatory and Uniform Auctions with an Unknown Number of Bidders," Management Science, INFORMS, vol. 54(9), pages 1610-1623, September.
    6. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    7. 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.
    8. 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.
    9. 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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    Cited by:

    1. Lang, Matthias & Seel, Christian & Strack, Philipp, 2014. "Deadlines in stochastic contests," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 134-142.

    More about this item


    All-pay auction; War 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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