A solution for bargaining problems with coalition structure

In this paper we study the restriction, to the class of bargaining problems with coalition structure, of several values which have been proposed on the class of non-transferable utility games with coalition structure. We prove that all of them coincide with the solution independently studied in Chae and Heidhues [Chae, S., Heidhues, P., 2004. A group bargaining solution. Mathematical Social Sciences 48, 37–53] and Vidal-Puga [Vidal-Puga, J.J., 2005a. A bargaining approach to the Owen value and the Nash solution with coalition structure. Economic Theory 25, 679–701]. Several axiomatic characterizations and two non-cooperative mechanisms are proposed.