Serial cost sharing methods for multi-commodity situations

We consider ways to extend the serial cost sharing method (Moulin, ii., She nker, S., Serial cost sharing, Econometrica 60 (1992) 1009-1037; Moulin, ii ., Shenker, S., Average cost pricing versus serial cost sharing: An axiomat ic comparison, Journal of Economic Theory 64 (1992) 178-201) to a setting w here 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 a gents on their stand alone costs leads us to a serial extension that is a g eneralization of the axial rule (Sprumont, 1996). A characterization of thi s Radial Serial Rule is provided. As a consequence we find that, in contrar y to the more restrictive model of Sprumont (1996), in our setting the prop erties of Independence of Null Agents, Rank Independence of Irrelevant Agen ts together with Ordinality and the Serial Principle are incompatible. (C) 1998 Elsevier Science B.V. All rights reserved.