Consistent Cost Sharing

A new concept of consistency for cost sharing solutions is discussed, analyzed, and related to the homonymous property within the rationing context. The class of additive and consistent mechanisms is isomorphic to the class of consistent and monotonic rationing methods. Consequently average and serial cost sharing are consistent, whereas Shapley-Shubik is not. Average cost sharing is the only strongly consistent element in this class. Examples are given how the extensive literature on consistent monotonic rationing can be inferred to study and characterize cost sharing mechanisms. A new class of incremental mechanisms is discussed of which the consistent elements correspond to consistent piecewise linear rationing methods