Responsibility and cross-subsidization in cost sharing

We propose two cost-sharing theories in which agents demand comparable commodities and are responsible for their own demand. Under partial responsibility, agents are not responsible for the asymmetries of the cost function: two agents consuming the same quantity pay the same price; this holds under full responsibility only if the cost function is symmetric. If the cost function is additively separable, each agent pays her stand-alone cost under full responsibility; this holds under partial responsibility only if the cost function is also symmetric. We generalize Moulin and Shenker's Distributivity axiom to cost-sharing methods for heterogeneous goods [Moulin, H., Shenker, S., 1999. Distributive and additive costsharing of an homogeneous good. Games Econ. Behav. 27, 299-330]. The subsidy-free serial method [Moulin, H., 1995. On additive methods to share joint costs. Japan. Econ. Rev. 46, 303-332] is essentially the only distributive method meeting Ranking and Dummy. The cross-subsidizing serial method [Sprumont, Y., 1998. Ordinal cost sharing. J. Econ. Theory 81, 126-162] is the only distributive method satisfying Separability and Strong Ranking. We propose an alternative characterization of the latter method based on a strengthening of Distributivity.