The bargaining set and coalition formation

We study solution concepts for nontransferable utility games according to which the coalition structure and the payoff allocations are simultaneously determined. The steady bargaining set is a refinement of the Zhou bargaining set, which is included in the Mas-Colell bargaining set. We prove the nonemptiness and partial efficiency of the steady bargaining set for at least one coalition structure under the restrictive non-crossing condition. Without this condition, the Zhou bargaining set may be empty and the Mas-Colell bargaining set is nonempty but may not be efficient.