In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened : we introduce a measure allowing to...

In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened : we introduce a measure allowing to...

One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of a Euclidean space, and not only polytopes. This rests on a fixed point result of Toussaint

This paper provides a fixed point theorem à la Schauder, where the mappings considered are possibly discontinuous. Our main result generalizes and unifies several well-known results.

One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of $\R^n$, and not only polytopes. This fixed point theorem can be applied to the problem of Nash equilibrium...

This paper provides a fixed point theorem à la Schauder, where the mappings considered are possibly discontinuous. Our main result generalizes and unifies several well-known results.