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An extension of Reny's theorem without quasiconcavity

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Author Info
Philippe Bich () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
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

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00323348_v1.

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Date of creation: 20 Sep 2008
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Handle: RePEc:hal:cesptp:halshs-00323348_v1

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Related research
Keywords: Nash equilibrium; existence; discontinuous games; non quasiconcave;

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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. [Downloadable!] (restricted)
  2. Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Blackwell Publishing, vol. 60(4), pages 935-48, October. [Downloadable!] (restricted)
  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, vol. 18(3), pages 247-59.
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