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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. 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

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 125 (2005)
Issue (Month): 1 (November)
Pages: 1-35

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Handle: RePEc:eee:jetheo:v:125:y:2005:i:1:p:1-35

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Web page: http://www.elsevier.com/locate/inca/622869

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

References

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1. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
   
   • Sprumont, Y., 1996. "Ordinal Cost Sharing," Cahiers de recherche 9624, Universite de Montreal, Departement de sciences economiques.
   • Sprumont, Y., 1996. "Ordinal Cost Sharing," Cahiers de recherche 9624, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
2. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
3. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
4. MOULIN, Hervé & SPRUMONT, Yves., 2002. "Responsibility and Cross-Subsidization in Cost Sharing," Cahiers de recherche 2002-19, Universite de Montreal, Departement de sciences economiques.
   
   • Moulin, Herve & Sprumont, Yves, 2006. "Responsibility and cross-subsidization in cost sharing," Games and Economic Behavior, Elsevier, vol. 55(1), pages 152-188, April.
   • Moulin, Herve & Sprumont, Yves, 2002. "Responsibility and Cross-Subsidization in Cost Sharing," Working Papers 2002-05, Rice University, Department of Economics.
5. Moulin, Herve & Sprumont, Yves, 2003. "On Demand Responsiveness in Additive Cost Sharing," Working Papers 2003-10, Rice University, Department of Economics.
   
   • Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
   • Moulin, Herve & Sprumont, Yves, 2004. "On Demand Responsiveness in Additive Cost Sharing," Working Papers 2004-03, Rice University, Department of Economics.
6. Eric Friedman & Moulin, Herve, 1995. "Three Methods to Share Joint Costs or Surplus," Working Papers 95-38, Duke University, Department of Economics.
   
   • 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.
7. Sprumont, Yves & Zhou, Lin, 1999. "Pazner-Schmeidler rules in large societies," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 321-339, April.
8. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
   
   • Martin Shubik, 1961. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Cowles Foundation Discussion Papers 112, Cowles Foundation for Research in Economics, Yale University.
9. Antonio Villar Notario & Carmen Herrero Blanco & Michael Maschler, 1996. "Individual rights and collective responsibility: The rights-egalitarian solution," Working Papers. Serie AD 1996-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
   
   • 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.
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, 2000. "Coherent Cost-Sharing Rules," Games and Economic Behavior, Elsevier, vol. 33(1), pages 126-144, October.
    
    • SPRUMONT, Yves, 1999. "Coherent Cost-Sharing Rules," Cahiers de recherche 9902, Universite de Montreal, Departement de sciences economiques.
12. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
13. William Thomson, 1999. "Welfare-domination under preference-replacement: A survey and open questions," Social Choice and Welfare, Springer, vol. 16(3), pages 373-394.
14. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
15. 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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Citations

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Cited by:

1. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
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.
3. SPRUMONT, Yves, 2004. "Nearly Serial Sharing Methods," Cahiers de recherche 17-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
   
   • Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer, vol. 37(2), pages 155-184, June.
   • SPRUMONT, Yves, 2004. "Nearly Serial Sharing Methods," Cahiers de recherche 2004-14, Universite de Montreal, Departement de sciences economiques.
4. Moulin, Herve & Sprumont, Yves, 2004. "On Demand Responsiveness in Additive Cost Sharing," Working Papers 2004-03, Rice University, Department of Economics.
   
   • Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
   • Moulin, Herve & Sprumont, Yves, 2003. "On Demand Responsiveness in Additive Cost Sharing," Working Papers 2003-10, Rice University, Department of Economics.
5. 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.
6. María Gómez-Rúa, 2012. "Sharing a polluted river network through environmental taxes," Economics Bulletin, AccessEcon, vol. 32(1), pages 992-1000.
7. MOULIN, Hervé & SPRUMONT, Yves, 2005. "Fair Allocation of Production Externalities: Recent Results," Cahiers de recherche 28-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
   
   • Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 0(1), pages 7-36.
   • SPRUMONT, Yves & MOULIN, Hervé, 2005. "Fair Allocation of Production Externalities: Recent Results," Cahiers de recherche 2005-22, Universite de Montreal, Departement de sciences economiques.
8. Yves Sprumont, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Econometrica, Econometric Society, vol. 78(5), pages 1711-1748, 09.
   
   • SPRUMONT, Yves, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Cahiers de recherche 01-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
   • SPRUMONT, Yves, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Cahiers de recherche 2010-01, Universite de Montreal, Departement de sciences economiques.
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. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.

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