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On Demand Responsiveness in Additive Cost Sharing

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  • Moulin, Herve

    (Rice U)

  • Sprumont, Yves

    (Universite de Montreal)

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. We explore their impact on the so-called full responsibility theory, postulating the standard Separability axiom, and on the partial responsibility theory postulating Strong Ranking, the requirement that the ranking of cost shares should never contradict that of demands. Under Separability, neither the Aumann-Shapley nor the Shapley-Shubik method is group monotonic; on the other hand, 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 cost functions and adding the standard Monotonicity characterizes the fixed-flow methods, containing the Shapley-Shubik and serial methods. The combination of Strong Ranking (partial responsibility), Solidarity and Monotonicity characterizes the quasi-proportional methods, under which cost shares are proportional to 'rescaled' demands.

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Bibliographic Info

Paper provided by Rice University, Department of Economics in its series Working Papers with number 2003-10.

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Date of creation: Oct 2003
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Handle: RePEc:ecl:riceco:2003-10

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  1. SPRUMONT, Yves, 1999. "Coherent Cost-Sharing Rules," Cahiers de recherche 9902, Universite de Montreal, Departement de sciences economiques.
  2. Sprumont, Y., 1996. "Ordinal Cost Sharing," Cahiers de recherche 9624, Universite de Montreal, Departement de sciences economiques.
  3. Moulin, Herve & Sprumont, Yves, 2006. "Responsibility and cross-subsidization in cost sharing," Games and Economic Behavior, Elsevier, vol. 55(1), pages 152-188, April.
  4. 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.
  5. William Thomson, 1999. "Welfare-domination under preference-replacement: A survey and open questions," Social Choice and Welfare, Springer, vol. 16(3), pages 373-394.
  6. Moulin, Herve & Sprumont, Yves, 2004. "On Demand Responsiveness in Additive Cost Sharing," Working Papers 2004-03, Rice University, Department of Economics.
  7. 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.
  8. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
  9. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
  10. 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.
  11. Sprumont, Yves & Zhou, Lin, 1999. "Pazner-Schmeidler rules in large societies," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 321-339, April.
  12. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
  13. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  14. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
  15. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
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Citations

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Cited by:
  1. Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer, vol. 36(3), pages 379-405, September.
  2. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
  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.
  4. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
  5. SPRUMONT, Yves, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Cahiers de recherche 01-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer, vol. 42(2), pages 439-460, May.
  7. SPRUMONT, Yves, 2004. "Nearly Serial Sharing Methods," Cahiers de recherche 2004-14, Universite de Montreal, Departement de sciences economiques.
  8. Eric Bahel & Christian Trudeau, 2013. "Independence of dummy units and Shapley-Shubik methods in cost sharing problems with technological cooperation," Working Papers 1304, University of Windsor, Department of Economics.
  9. Larrea, C. & Santos, J.C., 2007. "A characterization of the pseudo-average cost method," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 140-149, March.
  10. María Gómez-Rúa, 2012. "Sharing a polluted river network through environmental taxes," Economics Bulletin, AccessEcon, vol. 32(1), pages 992-1000.
  11. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
  12. Eric Bahel, 2011. "The implications of the ranking axiom for discrete cost sharing methods," International Journal of Game Theory, Springer, vol. 40(3), pages 551-589, August.

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