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Tournaments with reserve performance

Author

Listed:
  • Mikhail Drugov

    (New Economic School and CEPR)

  • Dmitry Ryvkin

    (Department of Economics, Florida State University)

  • Jun Zhang

    (Economics Discipline Group, School of Business, University of Technology Sydney)

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

  • Mikhail Drugov & Dmitry Ryvkin & Jun Zhang, 2022. "Tournaments with reserve performance," Working Papers wp2022_03_01, Department of Economics, Florida State University.
    • Handle: RePEc:fsu:wpaper:wp2022_03_01
    as

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    File URL: https://coss.fsu.edu/econpapers/wpaper/wp2022_03_01.pdf
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    References listed on IDEAS

    as
    1. Joaquín Poblete & Daniel Spulber, 2012. "The form of incentive contracts: agency with moral hazard, risk neutrality, and limited liability," RAND Journal of Economics, RAND Corporation, vol. 43(2), pages 215-234, June.
    2. Kirkegaard, René, 2017. "A unifying approach to incentive compatibility in moral hazard problems," Theoretical Economics, Econometric Society, vol. 12(1), January.
    3. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
    4. 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.
    5. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    Full references (including those not matched with items on IDEAS)

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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

    Keywords

    tournament; reserve performance; prize sharing;
    All these keywords.

    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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