EQUILIBRIA OF NONCOMPACT GENERALIZED GAMES AND NONCOMPACT QUASI-VARIATIONAL INEQUALITIES

In this paper, by the approximation theorem for the upper semicontinuous correspondence due to Tulcea(45) existence theorems of non-compact equilibria for generalized games are given when constraint correspondences are upper semicontinuous instead of having lower (upper) open sections or open graphs in infinite dimensional locally convex spaces. These results generalize many of existence theorems of equilibria for generalized games by relaxing the compactness of strategy spaces and by weakening the continuity of constraint correspondences. As applications of equilibria of non-compact generalized games, some non-compact quasi-variational inequalities are obtained which in turn imply existence theorems of solutions for non-compact generalized quasi-variational inequalities. Finally, one existence theorem for constrained games is derived by quasi-variational inequalities.