Maximal Elements and Equilibria of Generalized Games for Condensing Correspondences

In this paper, we first obtain some fixed point theorems in locally convex topological vector spaces which in turn imply some existence theorems of maximal elements for C-condensing correspondences. Then by employing approximation methods, we prove some existence theorems of equilibria for generalized games in which the constraint correspondences are C-condensing and lower or upper semicontinuous instead of having open lower sections or open graphs in infinite dimensional locally convex topological vector spaces. Finally, an existence theorem for the N-person game is also given. In particular, the corresponding results in the literature have been improved