Fair allocation of production externalities: recent results

We review recent results from the axiomatic theory of cost sharing. A method of sharing divides the total cost of a service between users based on the profile of their consumption and the cost function. In general, the total cost depends on asymmetrically individual consumption. We discuss two radically different normative interpretations of these asymmetries. According to the theory of full responsibility, each user is responsible for the cost resulting unquestionably its own supply and the cost shares must then reflect asymmetries of the cost function. According to the theory of partial responsibility, only the differences in the level of consumption may justify different cost share. We formulate the requirements of fairness and strategic stability through axioms of invariance and monotony. We examine the logical consistency of these axioms in the two theories above. In the approach of full responsibility, they allow us to characterize the three methods most often discussed in the literature: the Shapley and Shubik, the Aumann and Shapley and the classic serial method. In the context of partial responsibility, they lead to natural methods of proportional representation, and a variant of the serial method