Hadamard well-posedness in discontinuous non-cooperative games

We consider some recent classes of discontinuous games with Nash equilibria and we prove that such classes have the Hadamard well-posedness property. This means that given a game y, a net (y(alpha))(alpha) of games converging to y and a net (x(alpha))(alpha) such that x(alpha) is a Nash equilibrium of any y(alpha), then at least a cluster point of (x(alpha))(alpha) is a Nash equilibrium of y. In order to obtain this property, we prove that the map of Nash equilibria is upper sermcontinuous. Using the pseudocontinuity, a generalization of the continuity, we improve previous results obtained with continuous functions. (C) 2009 Elsevier Inc. All rights reserved.