On the constrained equilibrium problems with finite families of players

In this paper, we consider the equilibrium problem with finite number of families of players such that each family may not have the same number of players and finite number of families of constrained correspondences on the strategy sets. We also consider the case with two finite families of constrained correspondences on the strategies sets. We demonstrate an example of our equilibrium problem. We derive a fixed point theorem for a family of multimaps and a coincidence theorem for two families of multimaps. By using these results, we establish the existence of a solution of our equilibrium problems. The results of this paper generalize some known results in the literature.