Dominance network analysis of economic efficiency

This paper proposes an enhanced Dominance Network (DN) to assess the technical, economic and allocative efficiency of a set of Decision Making Units (DMUs). In a DN, the nodes represent DMUs and the arcs correspond to dominance relationships between them. Two types of dominance relationship are considered: technical and economic. The length of a technical dominance arc between two nodes is a weighted measure of the input and output differences between the two DMUs. The length of an economic dominance arc between two nodes corresponds to the cost, revenue or profit difference between them (depending on whether only unit input prices, unit output prices or both are known). The proposed dominance network is a multiplex network with two relations; the structure of both relations is similar. Thus, both of them are layered and their arcs have transitivity and additivity properties. However, since technical dominance implies economic dominance but not the reverse, economic dominance is more common and has a deeper structure. It may also have an underlying potential field so that the length of the arcs between any two nodes depends on the difference in their potentials and the direction of the arcs depends on the sign of that difference. Allocative inefficiencies can also be gauged on this DN. Complex network measures can be used to characterize and study this type of DN.