The bilateral consistent prekernel, the core, and NTU bankruptcy problems

It is shown that the bilateral consistent prekernel, an NTU solution concept that generalizes the Nash bargaining solution by means of a principle of bilateral consistency, is nonempty and intersects the core for a sufficiently rich class of NTU games: the class of boundary separating games, also introduced here. A second contribution of-this paper is the NTU extension of the bankruptcy games introduced by Aumann and Maschler (1985). These games, which provide a new approach for dealing with bargaining problems with claims, are shown to be boundary separating, so that the results apply.