DON and Shapley Value for Allocation among Cooperating Agents in a Network: Conditions for Equivalence

In a paper appearing in a recent issue of this journal ( Studies in Microeconomics), the authors explored a new method to allocate a divisible resource efficiently among cooperating agents located at the vertices of a connected undirected network. It was shown in that article that maximizing social welfare of the agents produces Pareto optimal allocations, referred to as dominance over neighbourhood (DON), capturing the notion of dominance over neighbourhood in terms of network degree. In this article, we show that the allocation suggested by the method competes well with current cooperative game-theoretic power centrality measures. We discuss the conditions under which DON turns exactly equivalent to a recent ‘fringe-based’ Shapley Value formulation for fixed networks, raising the possibility of such solutions being both Pareto optimal in a utilitarian social welfare maximization sense as well as fair in the Shapley value sense.