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...

Using the approach of Tian (2009) which characterizes the existence of Nash equilibria in strategic form games, we give sufficient conditions for the existence of Pareto efficient Nash equilibria in games where discontinuities on payoffs are allowed.

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...

In the recent paper by the author [Scalzo, V., 2010. Pareto efficient Nash equilibria in discontinuous games. Economics Letters 107, 364–365], a class of discontinuous games where efficient Nash equilibria exist has been defined. In the present paper, we complete the previous investigation and...

In this paper, a concept of approximate social Nash equilibria is considered and an existence result is given when the strategic spaces of the players are not compact. These have been obtained using an approximate fixed point theorem. As an application of the existence of such approximate social...

We introduce spaces of discontinuous games in which games having essential Nash equilibria are the generic case. In order to prove the existence of essential Nash equilibria in such spaces, we provide new results on the Ky Fan minimax inequality. In the setting of potential games, we show that...