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On Demand Responsiveness in Additive Cost Sharing

Listed author(s):
  • Moulin, Herve

    (Rice U)

  • Sprumont, Yves

    (Universite de Montreal)

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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File URL: http://www.ruf.rice.edu/~econ/faculty/Moulin/DemandResp.pdf
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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
Handle: RePEc:ecl:riceco:2003-10
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  1. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
  2. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
  3. Hervé Moulin, 1995. "On Additive Methods To Share Joint Costs," The Japanese Economic Review, Japanese Economic Association, vol. 46(4), pages 303-332, December.
  4. Baumol, William J, 1982. "Contestable Markets: An Uprising in the Theory of Industry Structure," American Economic Review, American Economic Association, vol. 72(1), pages 1-15, March.
  5. Moulin, Herve & Sprumont, Yves, 2006. "Responsibility and cross-subsidization in cost sharing," Games and Economic Behavior, Elsevier, vol. 55(1), pages 152-188, April.
  6. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
  7. 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.
  8. Sprumont, Yves & Zhou, Lin, 1999. "Pazner-Schmeidler rules in large societies," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 321-339, April.
  9. Hervé Moulin & Richard Stong, 2002. "Fair Queuing and Other Probabilistic Allocation Methods," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 1-30, February.
  10. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
  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.
  12. 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.
  13. Sprumont, Yves, 2000. "Coherent Cost-Sharing Rules," Games and Economic Behavior, Elsevier, vol. 33(1), pages 126-144, October.
  14. William Thomson, 1999. "Welfare-domination under preference-replacement: A survey and open questions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 373-394.
  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.
  16. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
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