Cost Sharing with Dependencies

Abstract: Two common assumptions in many works on cost sharing are 1. the lack of reciprocal production constraints; namely, it is assumed that if a bundle is to be produced then any "smaller" bundle can be produced, and 2. the cost function is (essentially) differentiable. This is obviously not the case in many cost problems of interest. Haimanko (2002,2003) addressed the second matter, but not the first, and his methods may not be extended to treat the first matter. We consider two classes of cost problems whose sets of producible bundles are centrally symmetric convex bodies, and whose cost functions are essentially non-differentiable. The cost functions in the first class are convex exhibiting non-decreasing marginal costs to scale, and those in the second class are piece-wise linear. We show existence and uniqueness of a cost allocation mechanism, satisfying standard axioms, on these classes. If time allows, generalizations of these results will be discussed.