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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. 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.

Suggested Citation

  • Moulin, Herve & Sprumont, Yves, 2004. "On Demand Responsiveness in Additive Cost Sharing," Working Papers 2004-03, Rice University, Department of Economics.
  • Handle: RePEc:ecl:riceco:2004-03
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    References listed on IDEAS

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    3. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
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    Cited by:

    1. Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(3), pages 379-405, September.
    2. Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 155-184, June.
    3. María Gómez-Rúa, 2012. "Sharing a polluted river network through environmental taxes," Economics Bulletin, AccessEcon, vol. 32(1), pages 992-1000.
    4. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    5. 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.
    6. Yves Sprumont, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Econometrica, Econometric Society, vol. 78(5), pages 1711-1748, September.
    7. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 439-460, May.
    8. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
    9. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
    10. EHLERS, Lars & WESTKAMP, Alexander, 2011. "Strategy-Proof Tie-Breaking," Cahiers de recherche 09-2011, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    11. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
    12. Eric Bahel, 2011. "The implications of the ranking axiom for discrete cost sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 551-589, August.
    13. Eric Bahel & Christian Trudeau, 2014. "Shapley–Shubik methods in cost sharing problems with technological cooperation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 261-285, August.
    14. 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.

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    JEL classification:

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

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