Existence d'un équilibre de Nash dans un jeu discontinu

Jean-Marc BONNISSEAU (), Pascal Gourdel and Hakim Hammami ()
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Hakim Hammami: CERMSEM, http://cermsem.univ-paris1.fr

Cahiers de la Maison des Sciences Economiques from Université Panthéon-Sorbonne (Paris 1)

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-continuous like in the second Reny's example. 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. (search for similar items in EconPapers)
JEL-codes: C69 C72 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2005-12
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Related works:
Working Paper: Existence d'un équilibre de Nash dans un jeu discontinu (2005)
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