The bilateral consistent prekernel, the core, and Non Transferable Utility bankruptcy problems

It is shown that the bilateral consistent prekernel, a Non Transferable Utility 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 Non Transferable Utility games: the class of boundary separating games, also introduced here. A second contribution of this paper is the Non Transferable Utility extension of the bankruptcy games introduced by Aumann and Maschler. 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.