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Existence d'un équilibre de Nash dans un jeu discontinu

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  • Jean-Marc Bonnisseau

    ()
    (CERMSEM)

  • Pascal Gourdel

    ()
    (CERMSEM)

  • Hakim Hammami

    ()
    (CERMSEM)

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.

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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b05099.

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Length: 7 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:mse:wpsorb:b05099

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Related research

Keywords: Discontinuous games; better-reply secure; Nash equilibrium; payoff security.;

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Cited by:
  1. Philippe Bich, 2006. "A constructive and elementary proof of Reny's theorem," Cahiers de la Maison des Sciences Economiques b06001, Université Panthéon-Sorbonne (Paris 1).

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