On the properties of solutions for non-transferable utility communication situations

We consider the model of cooperative games in which the agents can restrict the communication, because agents are sometimes divided into subgroups in a natural way, for example by their political affinities or by the companies that employ them. More particularly we focus on cooperative games with non-transferable utility, where the communication restrictions are represented by a graph defined on the set of agents. For this class of games we consider two solutions that are modifications of the Shapley value. We axiomatically characterize these two solutions and study their relation to the strong core.