Symmetry and approximate equilibria in games with countably many players

Abstract

I study games with countably many players, each of whom has finitely many pure strategies. The following are constructed: (i) a game that has a strong $$\epsilon $$ equilibrium for all $$\epsilon >0$$ but does not have a Nash equilibrium, and (ii) a symmetric game in which Nash equilibria exist, but all of them are asymmetric. Some additional results about infinite symmetric games are also derived.