On the discrete version of the Aumann-Shapley cost-sharing method

Each agent in a finite set requests an integer quantity of an idiosyncratic good; the resulting total cost must be shared among the participating agents. The Aumann-Shapley prices are given by the Shapley value of the game where each unit of each good is regarded as a distinct player. The Aumann-Shapley cost-sharing method charges to an agent the sum of the prices attached to the units she consumes. We show that this method is characterized by the two standard axioms of Additivity and Dummy, and the property of No Merging or Splitting: agents never find it profitable to split or to merge their consumptions. We offer a variant of this result using the No Reshuffling condition: the total cost share paid by a group of agents who consume perfectly substitutable goods depends only on their aggregate consumption. We extend this characterization to the case where agents are allowed to consume bundles of goods.