It is well known that in three-person transferable-utility cooperative games the bargaining set {\cal M}i1 and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which the...

We prove that the core of an assignment game (a two-sided matching game with transferable utility as introduced by Shapley and Shubik, 1972) is stable (i.e., it is the unique von Neumann-Morgenstern solution) if and only if there is a matching between the two types of players such that the...