Serial cost sharing methods for multi-commodity situations

Abstract

We consider ways to extend the serial cost sharing method (Moulin, H., Shenker, S., Serial cost sharing, Econometrica 60 (1992) 1009–1037; Moulin, H., Shenker, S., Average cost pricing versus serial cost sharing: An axiomatic comparison, Journal of Economic Theory 64 (1992) 178–201) to a setting where agents have a demand for bundles of heterogeneous goods. We introduce a class of serial extensions which is based on the use of preorderings. The class is characterized by the properties of Equal Treatment of Preordering Equivalents and the Radial Serial Principle. The preordering that judges agents on their stand alone costs leads us to a serial extension that is a generalization of the axial rule (Sprumont, 1996). A characterization of this Radial Serial Rule is provided. As a consequence we find that, in contrary to the more restrictive model of Sprumont (1996), in our setting the properties of Independence of Null Agents, Rank Independence of Irrelevant Agents together with Ordinality and the Serial Principle are incompatible.