Cooperative Optimality Concepts for Games with Preference Relations

In this paper we consider games with preference relations. The cooperative aspect of a game is connected with its coalitions. The main optimality concepts for such games are concepts of equilibrium and acceptance. We introduce a notion of coalition homomorphism for cooperative games with preference relations and study a problem concerning connections between equilibrium points (acceptable outcomes) of games which are in a homomorphic relation. The main results of our work are connected with finding of covariant and contrvariant homomorphisms.