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Zbl 0803.47059
Tan, Kok-Keong; Yuan, Zian-Zhi
A minimax inequality with applications to existence of equilibrium points. (English)
[J] Bull. Aust. Math. Soc. 47, No.3, 483-503 (1993). ISSN 0004-9727

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 $L\sb C$-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 $L\sb C$-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 $L\sb C$ 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 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
49J35 Minimax problems (existence)
91B50 Equilibrium in economics
91A44 Games involving topology or set theory

Keywords: minimax inequality; fixed point theorems; maximal elements for an $L\sb C$-majorized correspondence; maximal element theorem; existence theorems of equilibrium points; non-compact one-person game; non-compact qualitative game with $L\sb C$-majorized correspondences

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Zentralblatt MATH Berlin [Germany]