Communication Situations with a Hierarchical Player Partition

In this paper we study situations where agents who are divided in hierarchical classes have restricted possibilities for communication. We introduce a class of allocation rules for these situations inspired by the Myerson value (Myerson (1977)) and Shapley values with weight systems (Kalai and Samet (1988)). It is shown that this new class of allocation rules can be characterized by a consistency property, a fairness criterion, a property based on the hierarchy among the agents, and an eciency criterion. Furthermore, we show that the consistency property can be dropped from the axiomatic characterization when the fairness criterion is strengthened.