Working paper

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

Year:

2009

Published in:

SSRN
Discontinuous game
Payoff security
Transfer lower semicontinuity
Approximate Nash equilibrium
Reny's theorem

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.

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