Some Relaxed Solutions of Minimax Inequality for Discontinuous Game

2017 ◽  
pp. 86-97
Author(s):  
Xiaoling Qiu ◽  
Dingtao Peng
Keyword(s):  
Minimax Inequality ◽  
Discontinuous Game ◽  
Relaxed Solutions

scholarly journals A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces

2018 ◽  
Vol 179 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Marco Castellani ◽  
Massimiliano Giuli ◽  
Massimo Pappalardo
Keyword(s):  
Minimax Inequality ◽  
Finite Dimensional ◽  
Ky Fan Minimax Inequality ◽  
Ky Fan

A minimax inequality with applications to existence of equilibrium points

1993 ◽  
Vol 47 (3) ◽  
pp. 483-503 ◽  
Author(s):  
Kok-Keong Tan ◽  
Zian-Zhi Yuan
Keyword(s):  
Existence Theorems ◽  
Equilibrium Points ◽  
Vector Spaces ◽  
Minimax Inequality ◽  
Approximation Technique ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Person Game ◽  
Element Theorem

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 Lc-majorised 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 Lc-majorised correspondences are given. Using the latter result and employing an “approximation” technique used by Tulcea, we deduce equilibrium existence theorems for a non-compact generalised game with LC correspondences in topological vector spaces and in locally convex topological vector spaces. Our results generalise the corresponding results due to Border, Borglin-Keiding, Chang, Ding-Kim-Tan, Ding-Tan, Shafer-Sonnenschein, Shih-Tan, Toussaint, Tulcea and Yannelis-Prabhakar.

A Matching Theorem in GFC-Spaces with Application to Saddle Points

2013 ◽  
Vol 734-737 ◽  
pp. 2867-2870
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Saddle Point ◽  
Point Theorem ◽  
Saddle Points ◽  
Minimax Inequality ◽  
Saddle Point Theorem ◽  
Matching Theorem

In this paper, a matching theorem for weakly transfer compactly open valued mappings is established in GFC-spaces. As applications, a fixed point theorem, a minimax inequality and a saddle point theorem are obtained in GFC-spaces. Our results unify, improve and generalize some known results in recent reference.

scholarly journals On Fan's Minimax Inequality

1996 ◽  
Vol 201 (1) ◽  
pp. 103-113 ◽  
Author(s):  
Liang-Ju Chu
Keyword(s):  
Minimax Inequality
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