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Equilibrium analysis of the all-pay contest with two nonidentical prizes: Complete results

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  • Xiao, Jun

Abstract

This paper studies contests in which three or more players compete for two nonidentical prizes. The players have distinct constant marginal costs of performance or bid, which are commonly known. We show that the contests have a generically unique Nash equilibrium, and it is in mixed strategies. Moreover, we characterize the equilibrium payoffs and strategies in closed form. We also study how the equilibrium payoffs and strategies vary with the prizes. As an application, we numerically compute the optimal allocation of prizes that maximizes the total expected bid of asymmetric players.

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  • Xiao, Jun, 2018. "Equilibrium analysis of the all-pay contest with two nonidentical prizes: Complete results," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 21-34.
    • Handle: RePEc:eee:mateco:v:74:y:2018:i:c:p:21-34
    DOI: 10.1016/j.jmateco.2017.10.003
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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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    5. Yeon-Koo Che & Ian L. Gale, 2008. "Caps on Political Lobbying," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 337-345, Springer.
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    Cited by:

    1. Olszewski, Wojciech & Siegel, Ron, 2020. "Performance-maximizing large contests," Theoretical Economics, Econometric Society, vol. 15(1), January.
    2. Hwang, Sung-Ha & Koh, Youngwoo & Lu, Jingfeng, 2023. "Constrained contests with a continuum of battles," Games and Economic Behavior, Elsevier, vol. 142(C), pages 992-1011.
    3. 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.
    4. Mendel, Moritz & Pieroth, Ferdinand & Seel, Christian, 2021. "Your failure is my opportunity—Effects of elimination in contests," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    5. Xiao, Jun, 2023. "Ability grouping in contests," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    6. Andrzej Baranski & Sumit Goel, 2024. "Contest design with a finite type-space: A unifying approach," Papers 2410.04970, arXiv.org, revised Oct 2024.
    7. Chen Cohen & Ishay Rabi & Aner Sela, 2022. "Assortative Matching by Lottery Contests," Games, MDPI, vol. 13(5), pages 1-20, September.
    8. 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).

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    Keywords

    Asymmetric; Contest; Unique;
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