On the Concept of Middleman when Communication is Graph-Restricted

The aim of this paper is to present an approach to the middleman problem in the context of cooperative games when communication between players is graph-restricted. We consider a set of three axioms: linearity, dummy player and independence of non connected coalitions. These axioms are generally satisfied by solution concepts for games with communication structures which are extensions of the Shapley value, in the sense that they coincide with the Shapley value when the corresponding graph is complete.