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Optimal punishment in contests with endogenous entry

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  • Thomas, Jonathan P.
  • Wang, Zhewei

Abstract

We study optimal punishment in an all-pay contest with endogenous entry, where the participant with the lowest performance may be punished. When a small punishment is introduced, the lowest ability players drop out and those of medium ability exert less effort, while only the highest ability players exert more effort. A sufficient condition is given for the optimal punishment to be zero if the objective is to maximize the expected total effort. As cost functions become more convex, punishment becomes less desirable. When the objective is to maximize the expected highest individual effort, a positive punishment is desirable under much weaker conditions.

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  • Thomas, Jonathan P. & Wang, Zhewei, 2013. "Optimal punishment in contests with endogenous entry," Journal of Economic Behavior & Organization, Elsevier, vol. 91(C), pages 34-50.
    • Handle: RePEc:eee:jeborg:v:91:y:2013:i:c:p:34-50
    DOI: 10.1016/j.jebo.2013.02.007
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    3. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Song, Jian & Houser, Daniel, 2023. "Asymmetric shocks in contests: Theory and experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 216(C), pages 243-267.
    5. 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.
    6. Rusch, Hannes, 2023. "The logic of human intergroup conflict:," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. Aycinena, Diego & Rentschler, Lucas, 2019. "Entry in contests with incomplete information: Theory and experiments," European Journal of Political Economy, Elsevier, vol. 60(C).
    8. Yoshio Kamijo, 2014. "A theory of sanctions: Objectives, degree of heterogeneity, and growth potential matter for optimal use of carrot or stick," Working Papers SDES-2014-13, Kochi University of Technology, School of Economics and Management, revised Oct 2014.
    9. Liu, Bin & Lu, Jingfeng, 2023. "Optimal orchestration of rewards and punishments in rank-order contests," Journal of Economic Theory, Elsevier, vol. 208(C).
    10. Jia, Hao & Sun, Ching-jen, 2021. "The optimal entry fee-prize ratio in Tullock contests," Journal of Mathematical Economics, Elsevier, vol. 96(C).

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