Separation of joint plan equilibrium payoffs from the min-max functions. (Q1867025)

This paper concerns infinitely repeated and undiscounted two-person non-zero-sum games of incomplete information on one side. There are established sufficient conditions for the existence of an equilibrium with payoffs superior to what the players would receive from observable deviation. For this, it is shown that a no-where empty convex valued upper hemicontinuous correspondence from a compact metric space to a compact and convex subset of an Euclidean space can be approximated by Hausdorff-continuous convex valued correspondences that contain the original correspondence. This paper can be considered to be a first step toward a theory of equilibrium selection for these games. Examples are presented that show the difficulty and the desirability of some stronger results than those presented here.