On the existence of pure strategy Nash equilibria in large games

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 equicon-tinuous 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.