On additive methods to share joint costs

Moulin, H. (1995) On additive methods to share joint costs. Japanese Economic Review, 46(4), pp. 303-332. (doi: 10.1111/j.1468-5876.1995.tb00024.x)

Abstract

The Shapley value theory is extended to cost functions with multiple outputs (or to production functions with multiple inputs) where each output is demanded by a different agent and the level of demand varies. Beyond the Additivity and Dummy axioms (Shapley's original axioms) we insist that the cost-share of an agent should not decrease when she increases her demand (Demand Monotonicity). This property rules out the Aumann-Shapley pricing formula, as well as any method charging average cost for homogeneous goods.<p></p> We characterize the class of cost sharing methods satisfying Additivity, Dummy, Demand Monotonicity and Cross Monotonicity. The last says that when outputs i and j are cost complements (resp-cost substitutes) the cost share of i is non decreasing (resp-non increasing) in the demand of j.<p></p> Two prominent methods in the class are the Shapley-Shubik method (i.e. the Shapley value of the Stand Alone cost game) and serial cost sharing (which extends to multiple goods a formula due to Moulin and Shenker). They are characterized respectively by a lower bound and by an upper bound on individual cost shares.<p></p>

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Moulin, Professor Herve
• Authors: Moulin, H.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Japanese Economic Review
• ISSN: 1352-4739