This article is cited in 3 papers

Existence of stable coalition structures in four-person games

Fengyan  Sun^a, Elena Parilina<sup>bac

a</sup> St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia
^b Institute of Applied Mathematics of Shandong, Qingdao 266071, PR China
^c School of Mathematics and Statistics, Qingdao University, Qingdao 266071, PR China

Abstract: 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.

Keywords: coalition structure, stability, the Shapley value, the ES-value, four-player cooperative games.

Language: English