Abstract
In defining a bargaining set, it is desirable to require that a counterobjecting coalition has a non-empty intersection with the objecting coalition. We refer to this as the intersection property and define a bargaining set, MB 1 , that imposes this property on a variant of the bargaining set defined by Vohra (1991). To study the existence of MB 1 , a new version of the KKM theorem is proposed and the concept of a subbalanced game is introduced. We also provide conditions for the non-emptiness of MB 2 , a bargaining set introduced by Zhou (1994) which imposes the additional restriction that the objecting coalition not be a subset of the counterobjecting coalition. © 2006 Springer-Verlag.