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A Short Proof of Reny's Existence Theorem for Payoff Secure Games

By Pavlo Prokopovych

Abstract

A short proof of Reny (1999)'s equilibrium existence theorem for payoff secure games is provided. At the heart of the proof lies the concept of a multivalued mapping with the local intersection property. By means of the Fan-Browder collective fixed-point theorem, we show an approximate equilibrium existence theorem which covers a number of known games. Reny's theorem follows from it straightforwardly.Discontinuous game, payoff security, transfer lower semicontinuity, approximate Nash equilibrium, Reny's theorem

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