Convergence of discontinuous games and essential Nash equilibria

Abstract: Let Y be a topological space of non-cooperative games and let F be the map defined on Y such that F(y) is the set of all Nash equilibria of a game y. We are interested in finding conditions on the games which guarantee the upper semicontinuity of the map F. This property of F is a first requirement in order to study the existence of a dense subset Z of Y such that any game y belonging to Z has the following stability property: any Nash equilibria of the game y can be approached by Nash equilibria of a net of games converging to y