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Reward Design in Risk-Taking Contests

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  • Marcel Nutz
  • Yuchong Zhang

Abstract

Following the risk-taking model of Seel and Strack, $n$ players decide when to stop privately observed Brownian motions with drift and absorption at zero. They are then ranked according to their level of stopping and paid a rank-dependent reward. We study the problem of a principal who aims to induce a desirable equilibrium performance of the players by choosing how much reward is attributed to each rank. Specifically, we determine optimal reward schemes for principals interested in the average performance and the performance at a given rank. While the former can be related to reward inequality in the Lorenz sense, the latter can have a surprising shape.

Suggested Citation

  • Marcel Nutz & Yuchong Zhang, 2021. "Reward Design in Risk-Taking Contests," Papers 2102.03417, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2102.03417
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    References listed on IDEAS

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    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. Han Feng & David Hobson, 2014. "Gambling in contests with random initial law," Papers 1405.7801, arXiv.org, revised Feb 2016.
    3. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.
    4. Kempf, Alexander & Ruenzi, Stefan & Thiele, Tanja, 2009. "Employment risk, compensation incentives, and managerial risk taking: Evidence from the mutual fund industry," Journal of Financial Economics, Elsevier, vol. 92(1), pages 92-108, April.
    5. Seel, Christian, 2015. "Gambling in contests with heterogeneous loss constraints," Economics Letters, Elsevier, vol. 136(C), pages 154-157.
    6. Han Feng & David Hobson, 2016. "Gambling In Contests With Regret," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 674-695, July.
    7. Dawei Fang & Thomas Noe & Philipp Strack, 2020. "Turning Up the Heat: The Discouraging Effect of Competition in Contests," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1940-1975.
    8. Christian Seel & Philipp Strack, 2016. "Continuous Time Contests with Private Information," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1093-1107, August.
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    Cited by:

    1. Mark Whitmeyer, 2021. "Submission Fees in Risk-Taking Contests," Papers 2108.13506, arXiv.org.
    2. Marcel Nutz & Yuchong Zhang, 2021. "Mean Field Contest with Singularity," Papers 2103.04219, arXiv.org.

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