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A constructive and elementary proof of Reny's theorem

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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 proved the existence of Nash equilibria for better-reply-secure games, with possibly discontinuous payoff functions. Reny's proof is purely existential, and is similar to a contradiction proof: it gives non hint of a method to compute a Nash equilibrium in the class of games considered. In this paper, we adapt the arguments of Reny in order to obtain, for better-reply-secure games: an elementary proof of Nash equilibria existence, which is a consequence of Kakutani's theorem, and a "constructive" proof, in the sense that we obtain Nash equilibria as limits of fixed-point of well chosen correspondences.

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  • Philippe Bich, 2006. "A constructive and elementary proof of Reny's theorem," Post-Print halshs-00082760, HAL.
    • Handle: RePEc:hal:journl:halshs-00082760
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00082760
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    References listed on IDEAS

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    1. 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.
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    Keywords

    discontinuous payoffs; Reny's theorem;

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