In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.

New results on the variational stability of social Nash equilibria are obtained using the class of sequentially pseudocontinuous functions. This class of functions strictly includes the class of sequentially continuous functions and finds a natural motivation in the framework of Choice and...