It is well known that in three-person transferable-utility cooperative games the bargaining set M1i 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 bargaining set M1i (for the grand coalition) is larger than the core. This paper answers the equivalence question in the remaining four-person case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides with the bargaining set M1i. Our discussion employs a generalization of balancedness to games with coalition structures.
