Existence of Stable Coalition Structures in Three-player Games with Graph-constrained Solution

Abstract

The stability of coalition structures is investigated in the sense that no player prefers to individually deviate from the current coalition considering his utility. This principle is close to the concept of the Nash equilibrium. The evaluation of each player’s utility is determined with respect to the solution concept– the Shapley value with exogenous directed graph constraint. The existence of a stable coalition structure with respect to such a solution is examined for two-player as well as three-player games.