Large Games with a Finite Number of Classes and Nash’s ‘Improved’ Proof

Abstract

Nash (1951) proved the existence of mixed strategy Nash equilibria for finite games using Brouwer’s, rather than Kakutani’s, fixed point theorem. This paper adapts Nash’s (1951) proof to large games with a finite number of classes to establish the existence of pure strategy equilibria. The new approach sheds some light on the old results.