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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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    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. Gwen-Jiro Clochard & Guillaume Hollard & Julia Wirtz, 2022. "More effort or better technologies? On the effect of relative performance feedback," Bristol Economics Discussion Papers 22/767, School of Economics, University of Bristol, UK.
    3. Embrey, Matthew & Seel, Christian & Philipp Reiss, J., 2024. "Gambling in risk-taking contests: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 221(C), pages 570-585.
    4. Christian Seel, 2018. "Contests with endogenous deadlines," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 27(1), pages 119-133, March.
    5. Seel, Christian, 2015. "Gambling in contests with heterogeneous loss constraints," Economics Letters, Elsevier, vol. 136(C), pages 154-157.
    6. Seel, Christian & Stracky, Philipp, 2014. "Continuous Time Contests with Private Information," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100527, Verein für Socialpolitik / German Economic Association.
    7. Marcel Nutz & Yuchong Zhang, 2019. "A Mean Field Competition," Management Science, INFORMS, vol. 44(4), pages 1245-1263, November.
    8. Christian Seel & Philipp Strack, 2016. "Continuous Time Contests with Private Information," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1093-1107, August.
    9. Han Feng & David Hobson, 2014. "Gambling in contests with random initial law," Papers 1405.7801, arXiv.org, revised Feb 2016.
    10. Dmitry Ryvkin, 2022. "To Fight or to Give Up? Dynamic Contests with a Deadline," Management Science, INFORMS, vol. 68(11), pages 8144-8165, November.
    11. Nelson, Arthur B, 2020. "Deterrence in sequential contests: An experimental study," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 86(C).
    12. Marcel Nutz & Yuchong Zhang, 2021. "Mean Field Contest with Singularity," Papers 2103.04219, arXiv.org.
    13. Han Feng & David Hobson, 2013. "Gambling in contests with regret," Papers 1301.0719, arXiv.org.
    14. Marcel Nutz & Yuchong Zhang, 2021. "Reward Design in Risk-Taking Contests," Papers 2102.03417, arXiv.org, revised Nov 2021.
    15. Lang, Matthias & Seel, Christian & Strack, Philipp, 2014. "Deadlines in stochastic contests," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 134-142.
    16. Arthur B. Nelson, 2019. "Deterrence in sequential contests: An experimental study," Working Papers wp2019_11_02, Department of Economics, Florida State University.
    17. Gorno, Leandro & Iachan, Felipe S., 2020. "Competitive real options under private information," Journal of Economic Theory, Elsevier, vol. 185(C).
    18. Usvitskiy, Alexander, 2022. "Strategic risk-taking in dynamic contests," Journal of Economic Behavior & Organization, Elsevier, vol. 198(C), pages 511-534.

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    More about this item

    Keywords

    Discontinuous games; Contests; Relative performance pay; Risktaking behavior;
    All these keywords.

    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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