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.

The aim of the paper is to obtain the existence of equilibrium prices in economies where the excess demand correspondences—differently from the usual condition—are not necessarily upper semicontinuous. So, in our setting, we cannot use the Gale-Debreu-Nikaido Lemma. The existence of...