Existence d'un équilibre de Nash dans un jeu discontinu

Jean-Marc Bonnisseau, Pascal Gourdel () and Hakim Hammami ()
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Pascal Gourdel: CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Hakim Hammami: CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this paper, we present a more simple and independent proof of Reny's theorem (1998), on the existence of a Nash equilibrium in discontinue game, with a better-reply secure game in a Hausdorff topological vector space stronger than Reny's one. We will get the equivalence if the payoff function is upper semi-contineous like in the second Reny's exemple. Our proof is based on a new version of the existence of maximal element of Fan-Browder given by Deguire and Lassonde (1995). Reny's proof used a lemma of approximation of payoff function by a continuous sequence and show the existence of Nash equilibrium by the existence of equilibrium in mixed strategy proved in continuous game by the classical result.

Keywords: Discontinuous games; better-reply secure; Nash equilibrium; payoff security; Jeu discontinu; meilleur réponse sécurisée; équilibre de Nash; paiement sécurisé; théorème Fan Browder (search for similar items in EconPapers)
Date: 2005-12
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00173781v1
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Published in 2005

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Related works:
Working Paper: Existence d'un équilibre de Nash dans un jeu discontinu (2005)
Working Paper: Existence d'un équilibre de Nash dans un jeu discontinu (2005)
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