Existence of stable coalition structures in four-person games

Cooperative games with coalition structures are considered and the principle of coalition structure stability with respect to some cooperative solution concepts is determined. This principle is close to the concept of Nash equilibrium. The existence of a stable coalition structure with respect to the Shapley value and the equal surplus division value for the cases of two- and three-person games is proved. In this paper, the problem of existence of a stable coalition structure with respect to the Shapley value and the equal surplus division value for the case of four-person games with special characteristic function is examined.