Directed Communication Networks

In this paper we model the formation of directed communication networks.A directed communication network is represented by a directed graph.Firstly, we study an allocation rule satisfying two appealing properties, component efficiency and directed fairness.We show that such an allocation rule exists if and only if we restrict ourselves to a class of directed graphs that naturally comes to the fore in the setting of hierarchical structures.Subsequently, we discuss several possibilities to model the formation of directed communication networks and provide some preliminary results