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...

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.

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 present a new concept for (generalized) strategic form games, called \emph{doubly strong equilibrium}, and give an existence result when the players have non-ordered and discontinuous preferences. Since a doubly strong equilibrium is a strong equilibrium in the sense of Aumann, we get the...