Coalition Formation and Stability

This paper aims to develop, for any cooperative game, a solution notion that enjoys stability and consists of a coalition structure and an associated payoff vector derived from the Shapley value. To this end, two concepts are combined: those of strong Nash equilibrium and Aumann–Drèze coalitional value. In particular, we are interested in conditions ensuring that the grand coalition is the best preference for all players. Monotonicity, convexity, cohesiveness and other conditions are used to provide several theoretical results that we apply to numerical examples including real-world economic situations.