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Optimal prize-rationing strategy in all-pay contests with incomplete information

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  • Liu, Xuyuan
  • Lu, Jingfeng

Abstract

A contest organizer (e.g., a government regulatory agency) is endowed with the capacity to provide unlimited homogeneous prizes (e.g., medals) that he can use to incentivize contestants to exert productive effort in an all-pay auction with incomplete information. Each agent, at most, wins one prize. We study the optimal number of prizes the organizer should grant in order to induce maximal expected total effort or expected highest effort from agents. Both are single peaked under mild regularity conditions. When players’ abilities follow a family of beta distributions, expected highest effort maximization requires a smaller set of prizes to be awarded; for both goals, the optimal number of prizes weakly increases when the pool of contestants expands or contestant quality improves.

Suggested Citation

  • Liu, Xuyuan & Lu, Jingfeng, 2017. "Optimal prize-rationing strategy in all-pay contests with incomplete information," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 57-90.
    • Handle: RePEc:eee:indorg:v:50:y:2017:i:c:p:57-90
    DOI: 10.1016/j.ijindorg.2016.10.004
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    References listed on IDEAS

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    1. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
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    Citations

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    Cited by:

    1. Chen Cohen & David Lagziel & Ofer Levi & Aner Sela, 2020. "All-Pay Auctions With Heterogeneous Prizes And Partially Asymmetric Players," Working Papers 2010, Ben-Gurion University of the Negev, Department of Economics.
    2. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    3. Sumit Goel, 2022. "Optimal grading contests," Papers 2205.05207, arXiv.org, revised Sep 2023.
    4. Cohen, Chen & Lagziel, David & Levi, Ofer & Sela, Aner, 2023. "The role of the second prize in all-pay auctions with two heterogeneous prizes," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    5. Dahm, Matthias, 2018. "Semi-targeted all-pay auctions: A partial exclusion principle," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 256-282.
    6. Leppälä, Samuli, 2021. "A partially exclusive rent-seeking contest," Journal of Economic Behavior & Organization, Elsevier, vol. 187(C), pages 60-75.
    7. Vladimir Petkov, 2023. "Prize formation and sharing in multi-stage contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 259-289, January.
    8. 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.
    9. Wasser, Cédric & Zhang, Mengxi, 2023. "Differential treatment and the winner's effort in contests with incomplete information," Games and Economic Behavior, Elsevier, vol. 138(C), pages 90-111.

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    More about this item

    Keywords

    Multi-prize contest; Prize rationing; All-pay auction; Incomplete information;
    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
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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