Abstract The aim of this article is to present a new value of a cooperative game for the case of limited communication between players. The communication system we consider may be represented by a simple graph, that is, only pairwise meetings can occur and some of them are not permitted. An associated game is defined and the value has to verify a consistency axiom. The generalization proposed here is different from the Myerson value, and it coincides with the Shapley value in the case of full communication. Journal of Economic LiteratureClassification Number: C71.