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A minimax inequality with applications to existence of equilibrium points. (English) Zbl 0803.47059
Summary: A new minimax inequality is first proved. As a consequence, five equivalent fixed point theorems are formulated. Next a theorem concerning the existence of maximal elements for an L C -majorized correspondence is obtained. By the maximal element theorem, existence theorems of equilibrium points for a non-compact one-person game and for a non-compact qualitative game with L C -majorized correspondences are given. Using the latter result and employing an “approximation” technique used by Tulcea, we deduce equilibrium existence theorems for a non-compact generalized game with L C correspondences in topological vector spaces and in locally convex topological vector spaces. Our results generalize the corresponding results due to Border, Borglin- Keiding, Chang, Ding-Kim-Tan, Ding-Tan, Shafer-Sonnenschein, Shih-Tan, Toussaint, Tulcea and Yannelis-Prabhakar.
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
49J35Minimax problems (existence)
91B50General equilibrium theory in economics
91A44Games involving topology or set theory