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Wars of attrition and all-pay auctions with stochastic competition

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  • Bos, Olivier

Abstract

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 2 ()
Pages: 83-91

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Handle: RePEc:eee:mateco:v:48:y:2012:i:2:p:83-91

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: All-pay auction; War of attrition; Number of bidders;

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References

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  1. Steven A. Matthews, 1985. "Comparing Auctions for Risk Averse Buyers: A Buyer's Pointof View," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 664R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Harstad, Ronald M. & Kagel, John H. & Levin, Dan, 1990. "Equilibrium bid functions for auctions with an uncertain number of bidders," Economics Letters, Elsevier, Elsevier, vol. 33(1), pages 35-40, May.
  4. Jacob K. Goeree & Emiel Maasland & Sander Onderstal & John L. Turner, 2005. "How (Not) to Raise Money," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 113(4), pages 897-926, August.
  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, Elsevier, vol. 62(2), pages 476-508, March.
  6. Aleksandar Saša Peke\v{c} & Ilia Tsetlin, 2008. "Revenue Ranking of Discriminatory and Uniform Auctions with an Unknown Number of Bidders," Management Science, INFORMS, INFORMS, vol. 54(9), pages 1610-1623, September.
  7. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, Elsevier, vol. 72(2), pages 343-362, February.
  8. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, Elsevier, vol. 43(1), pages 1-19, October.
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Cited by:
  1. Lang, Matthias & Seel, Christian & Strack, Philipp, 2014. "Deadlines in stochastic contests," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 52(C), pages 134-142.

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