The bargaining set of four-person balanced games

Abstract

Listen

Translate article

It is well known that in three-person transferable-utility cooperative games the bargaining set ℳi 1 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 ℳi 1 (for the grand coalition) is larger then 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 ℳi 1. Our discussion employs a generalization of balancedness to games with coalition structures.