Maximal elements and equilibria of generalized games for 𝒰-majorized and condensing correspondences

Abstract

In this paper, we first give an existence theorem of maximal elements for a new type of preference correspondences which are 𝒰-majorized. Then some existence theorems for compact (resp., non-compact) qualitative games and generalized games in which the constraint or preference correspondences are 𝒰-majorized (resp., Ψ-condensing) are obtained in locally convex topological vector spaces.

Keywords

• Ψ-condensing mappings
• 𝒰 class
• 𝒰-majorized
• open lower sections
• lower semicontinuous
• upper semicontinuous
• fixed point
• mathematical economics
• maximal element
• selection theorem
• equilibrium point
• abstract economy
• generalized game.