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Optimal orchestration of rewards and punishments in rank-order contests

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  • Liu, Bin
  • Lu, Jingfeng

Abstract

We allow negative prizes and investigate effort-maximizing prize design in rank-order contests with incomplete information. Endogenous participation arises due to less-efficient types' incentive to avoid punishments. The optimum features winner-take-all for the best performer and at most one punishment for the worst performer among all potential contestants, whenever they enter the competition. Based on this, we then (1) provide a necessary and sufficient condition for the optimality of pure winner-take-all without punishment; and (2) show that the optimal entry threshold increases with the total number of contestants and converges to the Myerson cutoff in the limit. Finally, we characterize the optimal entry-dependent prize structure, allowing the prize sequence to vary with the number of entrants. The optimal design must entail endogenous entry, and it harmonically integrates both winner-take-all and egality.

Suggested Citation

  • Liu, Bin & Lu, Jingfeng, 2023. "Optimal orchestration of rewards and punishments in rank-order contests," Journal of Economic Theory, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:jetheo:v:208:y:2023:i:c:s0022053122001843
    DOI: 10.1016/j.jet.2022.105594
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    References listed on IDEAS

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    Cited by:

    1. Fupeng Sun & Yanwei Sun & Chiwei Yan & Li Jin, 2026. "Restricting entries to all-pay contests," International Journal of Game Theory, Springer;Game Theory Society, vol. 55(1), pages 1-46, June.
    2. Martin Grossmann, 2026. "Adjustment costs and fluctuations in competitions," Economica, London School of Economics and Political Science, vol. 93(369), pages 260-297, January.
    3. Aner Sela & Yizhaq Minchuk, 2024. "Carrots and sticks: collaboration of taxation and subsidies in contests," Working Papers 2407, Ben-Gurion University of the Negev, Department of Economics.
    4. Feng, Xin & Jiao, Qian & Kuang, Zhonghong & Lu, Jingfeng, 2024. "Optimal prize design in team contests with pairwise battles," Journal of Economic Theory, Elsevier, vol. 215(C).

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    Keywords

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    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • 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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