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Gambling in contests

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  • Seel, Christian
  • Strack, Philipp

Abstract

This paper presents a strategic model of risk-taking behavior in contests. Formally, we analyze an n-player winner-take-all contest in which each player decides when to stop a privately observed Brownian motion with drift. A player whose process reaches zero has to stop. The player with the highest stopping point wins. Unlike the explicit cost for a higher stopping time in a war of attrition, here, higher stopping times are riskier, because players can go bankrupt. We derive a closed-form solution of a Nash equilibrium outcome. In equilibrium, highest expected losses occur at an intermediate negative value of the drift.

Suggested Citation

  • Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:5:p:2033-2048
    DOI: 10.1016/j.jet.2013.07.005
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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. Park, Andreas & Smith, Lones, 2008. "Caller Number Five and related timing games," Theoretical Economics, Econometric Society, vol. 3(2), June.
    3. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    4. 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.
    5. Axel Anderson & Luís M. B. Cabral, 2007. "Go for broke or play it safe? Dynamic competition with choice of variance," RAND Journal of Economics, RAND Corporation, vol. 38(3), pages 593-609, September.
    6. Faruk Gul & Wolfgang Pesendorfer, 2012. "The War of Information," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 707-734.
    7. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
    8. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 1-21.
    9. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-960, July.
    10. Pedersen, J. L. & Peskir, G., 2001. "The Azéma-Yor embedding in non-singular diffusions," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 305-312, December.
    11. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
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    Cited by:

    1. Han Feng & David Hobson, 2013. "Gambling in contests with regret," Papers 1301.0719, arXiv.org.
    2. Han Feng & David Hobson, 2015. "Gambling in contests modelled with diffusions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 21-37, April.
    3. Lang, Matthias & Seel, Christian & Strack, Philipp, 2014. "Deadlines in stochastic contests," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 134-142.
    4. Seel, Christian, 2015. "Gambling in contests with heterogeneous loss constraints," Economics Letters, Elsevier, vol. 136(C), pages 154-157.
    5. 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.
    6. Han Feng & David Hobson, 2014. "Gambling in contests with random initial law," Papers 1405.7801, arXiv.org, revised Feb 2016.

    More about this item

    Keywords

    Discontinuous games; Contests; Relative performance pay; Risk-taking behavior;

    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
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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