A constructive and elementary proof of Reny's theorem
AbstractIn 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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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b06001.
Length: 8 pages
Date of creation: Jan 2006
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Reny's theorem; discontinuous payoffs.;
Find related papers by JEL classification:
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
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- Jean-Marc Bonnisseau & Pascal Gourdel & Hakim Hammami, 2005.
"Existence d'un équilibre de Nash dans un jeu discontinu,"
Cahiers de la Maison des Sciences Economiques
b05099, Université Panthéon-Sorbonne (Paris 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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