Sequentially Stable Coalition Structures

In this paper, we examine the questions of which coalition structure is formed and how payoãis distributed among players in cooperative games with externalities. We introduce a sequential stability concept called a sequentially stable payoãconåguration in a game with a coalition structure by extending the concept of the equilibrium binding agreements by Ray and Vohra (1997). Ray and Vohra capture explicitly the credibility of blocking coalitions, and then induce a recursive deånition of the stable coalition structures in a game with externalities. However, in their deånition, only breaking up is allowed for coalitions. We propose a new concept of a sequential stable payoã conåguration such that coalitions can both break up and merge into. The payoã conåguration z is said to sequentially dominate the payoãconåguration z0 if there is a sequence of payoãconågurations starting from z to z0 such that (1) in each step, two coalitions may merge or one coalition may break into two coalitions, and (2) in each step, the members in the merging coalitions or the breaking coalition prefer the payoãs of the ånal conåguration z0 to the present payoã.