Simple compatibility measures in symetric networks

An important class of social networks consists of exchange networks. These networks consist of a set of agents that each owns certain resources and a set of pairwise (symmetric) relations between these agents. The pairwise relations between the agents describe the possibilities to engage in binary exchange processes. The possibilities of the agents to obtain favourable resource bundles depend on their membership in a large number of the largest complete subnetworks in the exchange network. In this context the network power of an agent refers to the possibilities to obtain favourable exchange outcomes because of its cooperation power in the exchange network. In measuring power in such networks it is usual that the power of an agent increases if he has more neighbours that are mutually neighbours. We propose such a power measure: the class of simple compatibility measures, which reflects the compatibility power of the individual agents in the network and which we characterize by axioms.