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Equilibrium existence in contests with bid caps

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  • Olszewski, Wojciech
  • Siegel, Ron

Abstract

We prove equilibrium existence in distributional strategies for a general class of multiprize contests, including contests with bid caps. Contests with bid caps violate the assumptions of Reny’s (1999) equilibrium existence results as well as those of many other existence results. The equilibrium existence proof we provide for contests with bid caps refers to a special property of such contests, whereas the proof is much more straightforward for contests without a bid cap.

Suggested Citation

  • Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in contests with bid caps," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    • Handle: RePEc:eee:mateco:v:104:y:2023:i:c:s0304406822001306
    DOI: 10.1016/j.jmateco.2022.102804
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    References listed on IDEAS

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    1. Szech, Nora, 2015. "Tie-breaks and bid-caps in all-pay auctions," Games and Economic Behavior, Elsevier, vol. 92(C), pages 138-149.
    2. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
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    6. Olszewski, Wojciech & Siegel, Ron, 2019. "Bid caps in large contests," Games and Economic Behavior, Elsevier, vol. 115(C), pages 101-112.
    7. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    8. Carmona, Guilherme & Podczeck, Konrad, 2018. "Invariance of the equilibrium set of games with an endogenous sharing rule," Journal of Economic Theory, Elsevier, vol. 177(C), pages 1-33.
    9. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    10. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.
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    Cited by:

    1. Sela, Aner, 2023. "Two-stage elimination games," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    2. Levine, David K. & Mattozzi, Andrea & Modica, Salvatore, 2024. "The tripartite auction folk theorem," European Economic Review, Elsevier, vol. 162(C).

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