Cooperative games with coalition structures are considered and the principle of coalition structure stability with respect to 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 three person games is proved. We also consider a specific model of cooperative cost-saving game among banks as an application. In the model, the characteristic function assigning the cost-saving game has a special form. We also adopted the definition of stable coalition structure for the games with communication structure. The game with major player and hierarchical communication structure is considered. We also propose an approach of determining a stable coalition structure solving a stochastic game of a special form. Using Nash equilibrium in this game, we find out an analogy between the stable coalition structure and an absorbing state in a Markov chain. In addition, we consider the case of restricted coalitions assuming that not all coalitions are feasible and extend the definition of stable coalition structure to this case.
Groupe d’études et de recherche en analyse des décisions