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Continuous Time Contests with Private Information

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  • Seel, Christian
  • Stracky, Philipp

Abstract

This paper introduces a class of contest models in which each player decides when to stop a privately observed Brownian motion with drift and incurs costs depending on his stopping time. The player who stops his process at the highest value wins a prize. We prove existence and uniqueness of a Nash equilibrium outcome and derive the equilibrium distribution in closed form. As the variance tends to zero, the equilibrium outcome converges to the symmetric equilibrium of an all-pay auction. For two players and constant costs, each player's equilibrium pro fit decreases if the drift increases, the variance decreases, or the costs increase.

Suggested Citation

  • Seel, Christian & Stracky, Philipp, 2014. "Continuous Time Contests with Private Information," Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100527, Verein für Socialpolitik / German Economic Association.
  • Handle: RePEc:zbw:vfsc14:100527
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    References listed on IDEAS

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    1. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    2. Hugo A. Hopenhayn & Francesco Squintani, 2011. "Preemption Games with Private Information," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 667-692.
    3. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    4. Park, Andreas & Smith, Lones, 2008. "Caller Number Five and related timing games," Theoretical Economics, Econometric Society, vol. 3(2), June.
    5. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    6. Han Feng & David Hobson, 2014. "Gambling in contests with random initial law," Papers 1405.7801, arXiv.org, revised Feb 2016.
    7. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
    8. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    9. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
    10. 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.
    11. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
    12. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 1-21.
    13. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    14. 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.
    15. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
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    Cited by:

    1. Dmitry Ryvkin, 2020. "To fight or to give up? Dynamic contests with a deadline," Working Papers wp2020_07_01, Department of Economics, Florida State University.
    2. Philipp Denter & John Morgan & Dana (D.) Sisak, 2018. "Showing Off or Laying Low? The Economics of Psych-outs," Tinbergen Institute Discussion Papers 18-041/VII, Tinbergen Institute.
    3. Mendel, Moritz & Pieroth, Ferdinand & Seel, Christian, 2019. "Your Failure is My Opportunity - Eff ects of Elimination in Contests," Research Memorandum 016, Maastricht University, Graduate School of Business and Economics (GSBE).

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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