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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. Contrary to 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 the unique Nash equilibrium outcome of the game. In equilibrium, the trade-off between risk and reward causes a non-monotonicity: highest expected losses occur if the process decreases only slightly in expectation.

Suggested Citation

  • Seel, Christian & Strack, Philipp, 2012. "Gambling in Contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 375, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  • Handle: RePEc:trf:wpaper:375
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    File URL: https://epub.ub.uni-muenchen.de/13179/1/375.pdf
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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. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    3. 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.
    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. Faruk Gul & Wolfgang Pesendorfer, 2012. "The War of Information," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 707-734.
    6. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
    7. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 1-21.
    8. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-960, July.
    9. Park, Andreas & Smith, Lones, 2008. "Caller Number Five and related timing games," Theoretical Economics, Econometric Society, vol. 3(2), June.
    10. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
    11. 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.
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    Cited by:

    1. 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.
    2. Seel, Christian, 2015. "Gambling in contests with heterogeneous loss constraints," Economics Letters, Elsevier, vol. 136(C), pages 154-157.
    3. 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.
    4. Han Feng & David Hobson, 2014. "Gambling in contests with random initial law," Papers 1405.7801, arXiv.org, revised Feb 2016.
    5. Han Feng & David Hobson, 2013. "Gambling in contests with regret," Papers 1301.0719, arXiv.org.
    6. 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

    Keywords

    Discontinuous games; Contests; Relative performance pay; Risktaking 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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