A constructive and elementary proof of Reny's theorem

Philippe Bich ()
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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

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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.

Keywords: discontinuous payoffs; Reny's theorem (search for similar items in EconPapers)
Date: 2006-01
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Published in 2006

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