Network Structures with Hierarchy and Communication

Agents, participating in different kind of organizations, usually take different positions in some network structure. Two well-known network structures are hierarchies and communication networks. This paper aims at introducing a new type of network structure having both communication and hierarchical features. We describe a network by a collection of feasible sets, being the sets of network positions (nodes), that can organize themselves and act as a group. We introduce a new type of network structure, that has communication as well as hierarchical features. We compare these new network structures with other structures from the literature, and study its basis, i.e. the ‘smallest’ representation of the network. Finally, we apply these new network structures to cooperative games, where cooperation is restricted by some network structure, and provide an axiomatization of an extension of the Shapley value to this class of games.