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Optimal allocations of prizes and punishments in Tullock contests

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  • Aner Sela

    (Ben Gurion University of the Negev)

Abstract

We study Tullock contests with n symmetric players. We show that in a contest without an exit option, if prizes and punishments (negative prizes) have the same cost, it is optimal for the designer who wants to maximize the players’ total effort to allocate the entire prize sum to a single punishment without any prize. On the other hand, in a contest with an exit option, it is optimal to allocate the entire prize sum to a single prize and a single punishment, where independent of the costs of the prize and the punishment, the optimal value of the prize is larger than the optimal value of the punishment. We also show that allocating a prize and a punishment in a two-stage contest yields a higher expected total effort than in a one-stage contest.

Suggested Citation

  • Aner Sela, 2020. "Optimal allocations of prizes and punishments in Tullock contests," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 749-771, September.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:3:d:10.1007_s00182-020-00726-0
    DOI: 10.1007/s00182-020-00726-0
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    References listed on IDEAS

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    7. Noam Cohen & Guy Maor & Aner Sela, 2018. "Two-stage elimination contests with optimal head starts," Review of Economic Design, Springer;Society for Economic Design, vol. 22(3), pages 177-192, December.
    8. Fu, Qiang & Lu, Jingfeng & Wang, Zhewei, 2014. "“Reverse” nested lottery contests," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 128-140.
    9. Benny Moldovanu & Aner Sela & Xianwen Shi, 2012. "Carrots And Sticks: Prizes And Punishments In Contests," Economic Inquiry, Western Economic Association International, vol. 50(2), pages 453-462, April.
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    15. Kamijo, Yoshio, 2016. "Rewards versus punishments in additive, weakest-link, and best-shot contests," Journal of Economic Behavior & Organization, Elsevier, vol. 122(C), pages 17-30.
    16. Clark, Derek J. & Riis, Christian, 1998. "Influence and the discretionary allocation of several prizes," European Journal of Political Economy, Elsevier, vol. 14(4), pages 605-625, November.
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    Citations

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    Cited by:

    1. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    2. Yizhaq Minchuk & Aner Sela, 2021. "Subsidy and Taxation in All-Pay Auctions under Incomplete," Working Papers 2104, Ben-Gurion University of the Negev, Department of Economics.
    3. Chen Cohen & Ishay Rabi & Aner Sela, 2022. "Assortative Matching by Lottery Contests," Games, MDPI, vol. 13(5), pages 1-20, September.
    4. Aner Sela, 2022. "Ineffective Prizes In Multi-Dimensional Contests," Working Papers 2205, Ben-Gurion University of the Negev, Department of Economics.
    5. Minchuk, Yizhaq & Sela, Aner, 2023. "Subsidy and taxation in all-pay auctions under incomplete information," Games and Economic Behavior, Elsevier, vol. 140(C), pages 99-114.
    6. 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.
    7. David Lagziel & Lotem Ikan, 2023. "The Indoctrination Game," Working Papers 2304, Ben-Gurion University of the Negev, Department of Economics.
    8. Aner Sela & Amit Yeshayahu, 2022. "Contests with identity-dependent externalities," Working Papers 2203, Ben-Gurion University of the Negev, Department of Economics.
    9. Timothy Mathews & Soiliou Daw Namoro & James W. Boudreau, 2023. "The Impact of Organizer Market Structure on Participant Entry Behavior in a Multi-Tournament Environment," Games, MDPI, vol. 14(1), pages 1-21, January.
    10. Aner Sela, 2022. "Status Classification By Lottery Contests," Working Papers 2206, Ben-Gurion University of the Negev, Department of Economics.
    11. Aner Sela & Ishay Rabi & Chen Cohen, 2024. "Reputation in Contests," Working Papers 2409, Ben-Gurion University of the Negev, Department of Economics.
    12. Aner Sela & Ishay Rabi & Chen Cohen, 2023. "An Algorithmic Analysis of Parallel Contests," Working Papers 2317, Ben-Gurion University of the Negev, Department of Economics.
    13. Aner Sela, 2024. "Intermediate prizes in multi-dimensional contests," Theory and Decision, Springer, vol. 97(4), pages 721-743, December.

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    More about this item

    Keywords

    Tullock contests; Prizes; Punishments;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • 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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