On the constrained equilibrium problems with finite families of players. (Q1395866)

In this paper, the authors consider the equilibrium problem with a finite number of families of players such that each family may not have the same number of players and a finite number of families of constrained correspondences on the strategy sets. A fixed point theorem for a family of multimaps and a coincidence theorem for two families of multimaps are derived. The existence of a solution of the equilibrium problem with a finite number of families of players and a finite number of families of constraints on strategy sets are established. The authors also note that the Nash equilibrium theorem [\textit{J. Nash}, Ann. Math. (2) 54, 286--295 (1951; Zbl 0045.08202)] is a special case of their result. The results obtained in this paper also generalizes a result of \textit{L.-J. Lin} [Nonlinear Anal. 47, 637--648 (2001; Zbl 1042.91500)] which is derived using a fixed point theorem and a coincidence theorem.