This paper studies the existence of equilibrium solution concepts in a large class of economic models with discontinuous payoff functions. The issue is well understood for Nash equilibria, thanks to Reny’s better-reply security con- dition ( Reny 1999) and its recent improvements (Barelli and...

In this paper, we prove a fixed-point-like theorem for multi-valued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems : the fixed-point-like theorem by Hirsh, Magill, Mas-Colell (1990) or Husseiny,...

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...