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Axiomatic Cost and Surplis-Sharing

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Author Info
Moulin, Herve (Rice U)

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Abstract

The equitable division of a joint cost (or a jointly produced output) among agents with different shares or types of output (or input) commodities, is a central theme of the theory of cooperative games with transferable utility. Ever since Shapley's seminal contribution in 1953, this question has generated some of the deepest axiomatic results of modern microeconomic theory.More recently, the simpler problem of rationing a single commodity according to a profile of claims (reflecting individual needs, or demands, or liabilities) has been another fertile ground for axiomatic analysis. This rationing model is often called the bankruptcy problem in the literature.This chapter reviews the normative literature on these two models, and emphasizes their deep structural link via the Additivity axiom for cost sharing: individual cost shares depend additively upon the cost function. Loosely speaking, an additive cost-sharing method can be written as the integral of a rationing method, and this representation defines a linear isomorphism between additive cost-sharing methods and rationing methods.The simple proportionality rule in rationing thus corresponds to average cost pricing and to the Aumann-Shapley pricing method (respectively for homogeneous or heterogeneous output commodities). The uniform rationing rule, equalizing individual shares subject to the claim being an upper bound, corresponds to serial cost sharing. And random priority rationing corresponds to the Shapley-Shubik method, applying the Shapley formula to the Stand Alone costs.Several open problems are included. The axiomatic discussion of non-additive methods to share joint costs appears to be a promising direction for future research.

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Paper provided by Rice University, Department of Economics in its series Working Papers with number 2001-06.

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Date of creation: Aug 2001
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Handle: RePEc:ecl:riceco:2001-06

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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. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  2. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June. [Downloadable!] (restricted)
  3. Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September. [Downloadable!] (restricted)
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  4. Kolpin, Van, 1998. "Equitable Nonlinear Price Regulation: An Alternative Approach to Serial Cost Sharing," Games and Economic Behavior, Elsevier, vol. 22(1), pages 61-83, January. [Downloadable!] (restricted)
  5. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August. [Downloadable!] (restricted)
  6. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272. [Downloadable!] (restricted)
  7. Young, H Peyton, 1985. "Producer Incentives in Cost Allocation," Econometrica, Econometric Society, vol. 53(4), pages 757-65, July. [Downloadable!] (restricted)
  8. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August. [Downloadable!] (restricted)
  9. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September. [Downloadable!] (restricted)
  10. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520. [Downloadable!] (restricted)
  11. Angeles de Frutos, M., 1998. "Decreasing Serial Cost Sharing under Economies of Scale," Journal of Economic Theory, Elsevier, vol. 79(2), pages 245-275, April. [Downloadable!] (restricted)
  12. Moulin, Herve & Shenker, Scott, 1999. "Distributive and Additive Costsharing of an Homogeneous Good," Games and Economic Behavior, Elsevier, vol. 27(2), pages 299-330, May. [Downloadable!] (restricted)
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  13. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer, vol. 13(1), pages 51-59, January. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  15. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  16. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July. [Downloadable!] (restricted)
  17. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January. [Downloadable!] (restricted)
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  18. Nir Dagan & Oscar Volij, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," Economic theory and game theory 004, Nir Dagan. [Downloadable!]
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  19. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September. [Downloadable!] (restricted)
  20. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September. [Downloadable!] (restricted)
  21. Koster, Maurice & Tijs, Stef & Borm, Peter, 1998. "Serial cost sharing methods for multi-commodity situations," Mathematical Social Sciences, Elsevier, vol. 36(3), pages 229-242, December. [Downloadable!] (restricted)
  22. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April. [Downloadable!] (restricted)
  23. 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)
  24. Khmelnitskaya, Anna B., 1999. "Marginalist and efficient values for TU games," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 45-54, July. [Downloadable!] (restricted)
  25. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer, vol. 5(2), pages 229-46, March.
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  26. Sprumont, Yves, 2000. "Coherent Cost-Sharing Rules," Games and Economic Behavior, Elsevier, vol. 33(1), pages 126-144, October. [Downloadable!] (restricted)
  27. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August. [Downloadable!] (restricted)
  28. Kolpin, Van, 1996. "Multi-Product Serial Cost Sharing: An Incompatibility with the Additivity Axiom," Journal of Economic Theory, Elsevier, vol. 69(1), pages 227-233, April. [Downloadable!] (restricted)
  29. Hougaard, Jens Leth & Thorlund-Petersen, Lars, 2001. "Mixed serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 51-68, January. [Downloadable!] (restricted)
  30. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May. [Downloadable!] (restricted)
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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. Antonio Villar Notario & Juan D. Moreno Ternero, 2001. "The Tal-Family Of Rules For Bankruptcy Problems," Working Papers. Serie AD 2001-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
    Other versions:
  2. T. Marchant, 2004. "Rationing : dynamic considerations, equivalent sacrifice and links between the two approaches," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 04/244, Ghent University, Faculty of Economics and Business Administration. [Downloadable!]
  3. José M. Jiménez Gómez & María del Carmen Marco, 2008. "A New Approach for Bounding Awards in Bankruptcy Problems," Working Papers. Serie AD 2008-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  4. SPRUMONT, Yves, 2004. "Nearly Serial Sharing Methods," Cahiers de recherche 2004-14, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  5. R.I. Luttens, 2006. "Minimal rights based solidarity," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/356, Ghent University, Faculty of Economics and Business Administration. [Downloadable!]
  6. Juan de Dios Moreno Ternero & Antonio Villar Notario, 2003. "The Talmud Rule And The Securement Of Agents? Awards," Working Papers. Serie AD 2003-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
    Other versions:
  7. Juan de Dios Moreno Ternero & Antonio Villar Notario, 2002. "Bankruptcy Rules And Progressive Taxation," Working Papers. Serie AD 2002-15, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  8. Justin Leroux, 2006. "A discussion of the consistency axiom in cost-allocation problems," Cahiers de recherche 06-13, HEC Montréal, Institut d'économie appliquée. [Downloadable!]
  9. 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!]
  10. José Alcalde & José Angel Silva & María del Carmen Marco, 2002. "Bankruptcy Games And The Ibn Ezra'S Proposal," Working Papers. Serie AD 2002-28, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
    Other versions:
  11. Rene van den Brink & Yukihiko Funaki & Gerard van der Laan, 2008. "The Reverse Talmud Rule for Bankruptcy Problems," Tinbergen Institute Discussion Papers 08-026/1, Tinbergen Institute, revised 27 Mar 2008. [Downloadable!]
  12. Biung-Ghi Ju & Juan Moreno-Ternero, 2008. "On the equivalence between progressive taxation and inequality reduction," Social Choice and Welfare, Springer, vol. 30(4), pages 561-569, May. [Downloadable!] (restricted)
    Other versions:
  13. Herrero & C., 2004. "On the Adjudication of Conflicting Claims: An Experimental Study," Econometric Society 2004 North American Summer Meetings 166, Econometric Society. [Downloadable!]
  14. Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer, vol. 37(2), pages 155-184, June. [Downloadable!] (restricted)
  15. Juan Moreno-Ternero & Antonio Villar, 2006. "New characterizations of a classical bankruptcy rule," Review of Economic Design, Springer, vol. 10(2), pages 73-84, August. [Downloadable!] (restricted)
  16. Herve Moulin & Rakesh Vohra, 2003. "Characterization of Additive Cost Sharing Methods," Discussion Papers 1364, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  17. Jens Leth Hougaard & Lars Peter Østerdal, 2007. "Decreasing Serial Cost Sharing: an Axiomatic Characterization," Discussion Papers 07-02, University of Copenhagen. Department of Economics. [Downloadable!]
  18. Marco Mariotti, 2003. "Even Allocations For Generalised Rationing Problems," Working Papers. Serie AD 2003-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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