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Tournaments with Reserve Performance

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  • Drugov, Mikhail
  • Ryvkin, Dmitry
  • Zhang, Jun

Abstract

We study tournaments where winning a rank-dependent prize requires passing a reserve - a minimum performance standard. Agents' performance is determined by effort and noise. For log-concave noise distributions the optimal reserve is at the modal performance, and the optimal prize scheme is winner-take-all. In contrast, for log-convex noise distributions the optimal reserve is at the lower bound of the distribution of performance, which is passed with probability one in equilibrium, and it is optimal to award equal prizes to all qualifying agents. These pay schemes are optimal in a general class of symmetric monotone contracts that may depend on cardinal performance.

Suggested Citation

  • Drugov, Mikhail & Ryvkin, Dmitry & Zhang, Jun, 2022. "Tournaments with Reserve Performance," CEPR Discussion Papers 17107, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:17107
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    References listed on IDEAS

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    1. Qiang Fu & Jingfeng Lu, 2012. "Micro foundations of multi-prize lottery contests: a perspective of noisy performance ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 497-517, March.
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    4. Kirkegaard, René, 2017. "A unifying approach to incentive compatibility in moral hazard problems," Theoretical Economics, Econometric Society, vol. 12(1), January.
    5. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
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    Cited by:

    1. Liu, Bin & Lu, Jingfeng, 2023. "Optimal orchestration of rewards and punishments in rank-order contests," Journal of Economic Theory, Elsevier, vol. 208(C).

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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