An Axiomatic Characterization of a Class of Locations in Tree Networks

In this paper we describe four axioms that uniquely characterize the class of locations in tree networks that are obtained by minimizing an additively separable, nonnegative, nondecreasing, differentiable, and strictly convex function of distances. This result is analogous to results that have been obtained in the theory of bargaining, social choice, and fair resource allocation.