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Gambling in contests modelled with diffusions

Author

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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. Yeon-Koo Che & Ian L. Gale, 2008. "Caps on Political Lobbying," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 337-345, Springer.
    3. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
    4. , & , & ,, 2012. "Optimal deadlines for agreements," Theoretical Economics, Econometric Society, vol. 7(2), May.
    5. 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.
    6. Cohen Chen & Sela Aner, 2007. "Contests with Ties," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, December.
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    Cited by:

    1. Seel, Christian, 2015. "Gambling in contests with heterogeneous loss constraints," Economics Letters, Elsevier, vol. 136(C), pages 154-157.
    2. Whitmeyer, Mark, 2023. "Submission costs in risk-taking contests," Games and Economic Behavior, Elsevier, vol. 142(C), pages 101-112.
    3. Mark Whitmeyer, 2021. "Submission Fees in Risk-Taking Contests," Papers 2108.13506, arXiv.org.
    4. Adnan M. S. Fakir & Yiwei Qian & Naveen Sunder, 2023. "Gender Differences in Preference for Non-pecuniary Benefits in the Labour Market. Experimental Evidence from an Online Freelancing Platform.," Working Paper Series 0623, Department of Economics, University of Sussex Business School.
    5. Marcel Nutz & Yuchong Zhang, 2021. "Mean Field Contest with Singularity," Papers 2103.04219, arXiv.org.
    6. 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.
    7. Marcel Nutz & Yuchong Zhang, 2021. "Reward Design in Risk-Taking Contests," Papers 2102.03417, arXiv.org, revised Nov 2021.
    8. Hwang, Sung-Ha & Koh, Youngwoo & Lu, Jingfeng, 2023. "Constrained contests with a continuum of battles," Games and Economic Behavior, Elsevier, vol. 142(C), pages 992-1011.

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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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