Communication situations with asymmetric players

In this paper we study situations where asymmetric players have restricted possibilities for communication. Extreme asymmetry results in a hierarchy a mong the players. We introduce a class of allocation rules for these situat ions inspired by the Myerson value (Myerson (1977)) and Shapley values with weight systems (Kalai and Samet (1988)). It is shown that this new class o f allocation rules can be characterized by a consistency property, a fairne ss criterion, a property based on the hierarchy among the players, and an e fficiency criterion. Furthermore, we show that the consistency property can be dropped from the axiomatic characterization when the fairness criterion is strengthened.