The Coalitional Nash Bargaining Solution∗

The coalitional Nash bargaining solution is defined to be the core allocation for which the Nash product is maximal. We consider a non-cooperative model in which one team may form. The grand team, consisting of all players, generates the largest surplus. But a smaller team may form. We show that as players get more patient if an efficient and stationary equilibrium exists, it must deliver payoffs that correspond to the coalitional Nash bargaining solution. We also characterize when an efficient and stationary equilibrium exists. We find that existence requires conditions that go beyond the non-emptyness of the core.