Inverse of Berge’s maximum theorem in locally convex topological vector spaces and its applications

Abstract

Abstract In this paper, the inverse of Berge’s maximum theorem is established in a locally convex topological vector space. Using this result, the generalized Gale–Nikaido–Debreu’s lemma and the generalized coincidence point theorem are derived from the equilibrium theorem of generalized games. By combining the inverse of Berge’s maximum theorem with the generalized coincidence point theorem, the equilibrium theorem of the generalized game is obtained immediately. Finally, we show that Fan–Glicksberg’s fixed point theorem and von Neumann’s lemma can be derived directly from the coincidence point theorem.