Existence of equilibrium in generalized games with abstract convexity structure

The aim of this paper is to prove the existence of equilibrium for generalized games or abstract economies in contexts where the convexity conditions on strategy spaces and preference correspondences are relaxed and an arbitrary number of agents is considered. The results are based on a fixed-point theorem in which the convexity condition on sets and images of correspondences is replaced by a general notion of abstract convexity, called me-spaces, generalizing the notions of simplicial convexity, H-spaces, and G-convex spaces.