Potential, consistency, and cost allocation prices

In a typical cost allocation problem, a decision maker must allocate the joint cost of producing a specified vector of goods or services using prices. In earlier work, Billera, Heath, and Raanan applied the theory of values of nonatomic games of Aumann and Shapley to develop a pricing mechanism called Aumann–Shapley pricing. The Aumann–Shapley value for nonatomic games has an axiomatic foundation that was adapted to the cost allocation context by Billera and Heath and Mirman and Tauman. In this paper, we develop the notions of ‘reduced cost function’, ‘consistency’, and ‘potential’ for cost allocation problems and we provide a new axiomatic characterization of symmetric and weighted Aumann–Shapley pricing in terms of consistency.