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On Demand Responsiveness in Additive Cost Sharing

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Author Info
Moulin, Herve (Rice U)
Sprumont, Yves (Universite de Montreal)

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Abstract

We propose two new axioms of demand responsiveness for additive cost sharing with variable demands. Group Monotonicity requires that if a group of agents increase their demands, not all of them pay less. Solidarity says that if agent i demands more, j should not pay more if k pays less. Both axioms are compatible in the partial responsibility theory postulating Strong Ranking, i.e., the ranking of cost shares should never contradict that of demands. The combination of Strong Ranking , Solidarity and Monotonicity characterizes the quasi-proportional methods, under which cost shares are proportional to 'rescaled' demands. The alternative full responsibility theory is based on Separability, ruling out cross-subsidization when costs are additively separable. Neither the Aumann-Shapley nor the Shapley-Shubik method is group monotonic. On the otherhand, convex combinations of "nearby" fixed-path methods are group-monotonic: the subsidy-free serial method is the main example. No separable method meets Solidarity, yet restricting the axiom to submodular (or supermodular) cost functions leads to a characterization of the fixed-flow methods, containing the Shapley-Shubik and serial methods.

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Paper provided by Rice University, Department of Economics in its series Working Papers with number 2004-03.

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Date of creation: May 2004
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Handle: RePEc:ecl:riceco:2004-03

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C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

References listed on IDEAS
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  1. Friedman, Eric & Moulin, Herve, 1999. "Three Methods to Share Joint Costs or Surplus," Journal of Economic Theory, Elsevier, vol. 87(2), pages 275-312, August. [Downloadable!] (restricted)
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  2. William Thomson, 1999. "Welfare-domination under preference-replacement: A survey and open questions," Social Choice and Welfare, Springer, vol. 16(3), pages 373-394. [Downloadable!] (restricted)
  3. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August. [Downloadable!] (restricted)
  4. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July. [Downloadable!] (restricted)
  5. Sprumont, Yves & Zhou, Lin, 1999. "Pazner-Schmeidler rules in large societies," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 321-339, April. [Downloadable!] (restricted)
  6. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September. [Downloadable!] (restricted)
  7. Moulin Herve & Shenker Scott, 1994. "Average Cost Pricing versus Serial Cost Sharing: An Axiomatic Comparison," Journal of Economic Theory, Elsevier, vol. 64(1), pages 178-201, October. [Downloadable!] (restricted)
  8. Sprumont, Yves, 2000. "Coherent Cost-Sharing Rules," Games and Economic Behavior, Elsevier, vol. 33(1), pages 126-144, October. [Downloadable!] (restricted)
  9. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August. [Downloadable!] (restricted)
  10. Moulin, Herve & Sprumont, Yves, 2002. "Responsibility and Cross-Subsidization in Cost Sharing," Working Papers 2002-05, Rice University, Department of Economics. [Downloadable!]
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  11. Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999. "Individual rights and collective responsibility: the rights-egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 59-77, January. [Downloadable!] (restricted)
  12. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics. [Downloadable!]
  13. Martin Shubik, 1961. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Cowles Foundation Discussion Papers 112, Cowles Foundation, Yale University. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics. [Downloadable!]
  2. Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer, vol. 36(3), pages 379-405, September. [Downloadable!] (restricted)
  3. SPRUMONT, Yves & MOULIN, Hervé, 2005. "Fair Allocation of Production Externalities: Recent Results," Cahiers de recherche 2005-22, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  4. SPRUMONT, Yves, 2004. "Nearly Serial Sharing Methods," Cahiers de recherche 2004-14, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  5. Sprumont, Yves, 2004. "Aumann-Shapley Pricing: A Reconsideration of the Discrete Case," Cahiers de recherche 11-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
  6. Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer, vol. 37(2), pages 155-184, June. [Downloadable!] (restricted)
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