Existence Theorems of Equilibria in G-Convex Spaces for GLC-Majorized Correspondences

Abstract

A fixed point theorem is proved in G-convex spaces (introduced by Park and Kim [17]). As applications of the fixed point theorem some existence theorems of maximal elements for G^L_C correspondences and G^L_C majorized correspondences are obtained. Applying the existence theorems of maximal elements, some equilibrium existence theorems for one-person games, qualitative games and non-compact generalized games are given. These results are generalization, into G-convex spaces, of the corresponding results due to Border, Borglin-Keiding, Chang, Ding-Tan, Ding-Kim-Tan, Shafer-Sonnenschein, Tan-Yuan. Toussaint, Tulcea and Yannaelis-Prabhakar.