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)

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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.

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.

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.

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

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