Weighted Aumann-Shapley pricing

Cost allocation problems arise in many contexts in economics and management science. In a typical problem that we have in mind, a decision maker must decide how to allocate the joint cost of production among several commodities using prices. Furthermore, these prices must satisfy certain reasonable postulates among which is the requirement that total revenue associated with these prices must cover total cost. In this paper, we investigate a generalization of Aumann-Shapley pricing, called Weighted Aumann-Shapley pricing, that allows for asymmetric pricing of commodities even when those commodities affect costs in a symmetric fashion. Weighted AS pricing is a natural extension of (symmetric) Aumann-Shapley pricing, and may be considered a non-atomic analogue of Owen's modified diagonal formula (with respect to the multilinear extension) for the weighted TU Shapley Value.