On the Existence of Pure Strategy Nash Equilibria in Large Games

Abstract

We consider an asymptotic version of Mas-Colell’s theorem on the existence of pure strategy Nash equilibria in large games. Our result states that, if players’ payoff functions are selected from an equicontinuous family, then all sufficiently large games have an ε – pure, ε – equilibrium for all ε > 0. We also show that our result is equivalent to Mas-Colell’s existence theorem, implying that it can properly be considered as its asymptotic version.