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An extension of Reny's theorem without quasiconcavity

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  • Philippe Bich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened: roughly, we introduce a measure allowing to localize the lack of quasiconcavity; this allows to refine the analysis of equilibrium existence

Suggested Citation

  • Philippe Bich, 2008. "An extension of Reny's theorem without quasiconcavity," Working Papers halshs-00323348, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00323348
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00323348
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    References listed on IDEAS

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    1. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
    2. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    3. 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.
    4. Kostreva, M M, 1989. "Nonconvexity in Noncooperative Game Theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 247-259.
    5. Carolyn Pitchik, 1981. "Equilibria of a Two-Person Non-Zero Sum Noisy Game of Timing," Cowles Foundation Discussion Papers 579, Cowles Foundation for Research in Economics, Yale University.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Nash equilibrium; existence; discontinuous games; non quasiconcave;
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