Cost Allocation with Variable Production and the Shapley Value

Abstract

Cooperative game theory and cost allocation are tightly intertwined realms. On the one hand, key notions of the cooperative game theory have proved to be very useful for allocating common costs. On the other hand, practitioners in cost allocation foreshadowed central ideas of the cooperative game theory. In this chapter we give a brief overview of a particular instance of the relationship between these two elds. Speci cally we review the cost allocation rules inspired by the Shapley value and the Aumann-Shapley value, in situations in which the involved agents request variable demands. This review is exclusively made from a normative perspective. In the end cost allocation refers to practical problems in which settlements are based on reasonable principles of fairness. Thus we restrict our attention to the axiomatic characterizations of the considered allocation rules. Mainly two kinds of characterizations have been examined. The rst one is based on the property of additivity, saying that payments of different problems can be aggregated; and the second one on monotonicity requiring that when the marginal cost decreases a lower cost share must be assigned.