Working paper
A Short Proof of Reny's Existence Theorem for Payoff Secure Games
Year:
2009Published in:
SSRNDiscontinuous 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.