Equilibria of nonparacompact generalized games with [formula omitted]-majorized correspondences in FC-spaces

Abstract

The new concept of FC-hull for a nonempty subset in FC-spaces is introduced, which includes the convex hull in topological vector spaces, the H -convex hull in H -spaces and G -convex hull in G -convex spaces as special cases. On this basis, new classes of ℒ c -correspondences and ℒ c -majorized correspondences without open lower sections are introduced in FC-spaces. Some existence theorems of maximal elements for ℒ c -correspondences and ℒ c -majorized correspondences are proved in FC-spaces. As applications, some equilibrium existence theorems for qualitative games and generalized games with infinite set of players and ℒ c -majorized correspondences are established in FC-spaces. These results unify, improve and generalize many corresponding results in recent literature.