Coincidence theorems for families of multimaps and their applications to equilibrium problems

Abstract

We apply some continuous selection theorems to establish coincidence theorems for a family of multimaps under various conditions. Then we apply these coincidence theorems to study the equilibrium problem with $m$ families of players and $2m$ families of constraints on strategy sets. We establish the existence theorems of equilibria of this problem and existence theorem of equilibria of abstract economics with two families of players.