A constructive and elementary proof of Reny's theorem

Philippe Bich

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

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: Reny's theorem; discontinuous payoffs (search for similar items in EconPapers)
JEL-codes: C7 (search for similar items in EconPapers)
Pages: 8 pages
Date: 2006-01
New Economics Papers: this item is included in nep-gth
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Persistent link: https://EconPapers.repec.org/RePEc:mse:wpsorb:b06001

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