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Gambling in contests modelled with diffusions

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  • Han Feng
  • David Hobson

Abstract

In the Seel–Strack contest (J Econ Theory 148(5):2033–2048, 2013 ), $$n$$ n agents each privately observe an independent copy of a drifting Brownian motion which starts above zero and is absorbed at zero. Each agent chooses when to stop the process she observes, and the winner of the contest is the agent who stops her Brownian motion at the highest value. The objective of each agent is to maximise her probability of winning the contest. Seel and Strack derived a Nash equilibrium under a joint feasibility condition on the drift and the number of players. We consider a generalisation of the Seel–Strack contest in which the observed processes are independent copies of some time-homogeneous diffusion. This naturally leads us to consider the problem in cases where the analogue of the feasibility condition is violated. We solve the problem via a change of scale and a Lagrangian method. Unlike in the Seel–Strack problem, it turns out that the optimal strategy may involve a target distribution which has an atom, and the rule used for breaking ties becomes important. Copyright Springer-Verlag Italia 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:38:y:2015:i:1:p:21-37
    DOI: 10.1007/s10203-014-0156-3
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    References listed on IDEAS

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    1. Dechenaux, Emmanuel & Kovenock, Dan & Lugovskyy, Volodymyr, 2006. "Caps on bidding in all-pay auctions: Comments on the experiments of A. Rapoport and W. Amaldoss," Journal of Economic Behavior & Organization, Elsevier, vol. 61(2), pages 276-283, October.
    2. Cohen Chen & Sela Aner, 2007. "Contests with Ties," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, December.
    3. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-680, November.
    4. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
    5. Che, Yeon-Koo & Gale, Ian L, 1998. "Caps on Political Lobbying," American Economic Review, American Economic Association, vol. 88(3), pages 643-651, June.
    6. , & , & ,, 2012. "Optimal deadlines for agreements," Theoretical Economics, Econometric Society, vol. 7(2), May.
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    Cited by:

    1. Matthew Embrey & Christian Seel & J. Philipp Reiss, 2020. "Gambling in Risk-Taking Contests: Experimental Evidence," Working Paper Series 1620, Department of Economics, University of Sussex Business School.
    2. repec:sus:susewp:0623 is not listed on IDEAS
    3. Seel, Christian, 2015. "Gambling in contests with heterogeneous loss constraints," Economics Letters, Elsevier, vol. 136(C), pages 154-157.
    4. Marcel Nutz & Yuchong Zhang, 2021. "Mean Field Contest with Singularity," Papers 2103.04219, arXiv.org.
    5. Marcel Nutz & Yuchong Zhang, 2021. "Reward Design in Risk-Taking Contests," Papers 2102.03417, arXiv.org, revised Nov 2021.
    6. Mark Whitmeyer, 2021. "Submission Fees in Risk-Taking Contests," Papers 2108.13506, arXiv.org.

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    More about this item

    Keywords

    Seel–Strack contest; Nash equilibrium; Randomized strategies; Lagrangian method; Diffusions; Skorokhod embedding problem; C72; C73; D81;
    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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