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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.

Suggested Citation

  • 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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    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. Chen Cohen & Ishay Rabi & Aner Sela, 2022. "Assortative Matching by Lottery Contests," Games, MDPI, vol. 13(5), pages 1-20, September.
    3. 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).
    4. Olszewski, Wojciech & Siegel, Ron, 2020. "Performance-maximizing large contests," Theoretical Economics, Econometric Society, vol. 15(1), January.
    5. 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).
    6. Xiao, Jun, 2023. "Ability grouping in contests," Journal of Mathematical Economics, Elsevier, vol. 104(C).

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    Keywords

    Asymmetric; Contest; Unique;
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