A characterization of the pseudo-average cost method

We study the pseudo-average cost method in discrete and continuum cost allocation problems. This solution was introduced, in the discrete case, by Moulin (Moulin, H., 1995. On additive methods to share joint costs. The Japanese Economic Review 46, 303-332). In the continuous case, this solution has been introduced, asymptotically, by Larrea and Santos (Larrea, C., Santos, J.C., 2006. Cost allocation schemes: an asymptotic approach. Games and Economic Behavior 57, 63–72). Here we propose a characterization of this solution using an adaptation of the balanced contributions axioms, used by Myerson (Myerson, R., 1980. Conference structures and fair allocation rules. International Journal of Game Theory 9, 169-182) to characterize the Shapley value in TU games. The new axiom, in the continuous case, is the natural extension of the axiom used in the discrete case.