IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this book chapter

Axiomatic cost and surplus sharing

In: Handbook of Social Choice and Welfare

  • Moulin, Herve

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/B7P65-4FFPH86-B/2/6adef470ba7076122e74c0e924bd164f
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

as
in new window

This chapter was published in:
  • K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
  • This item is provided by Elsevier in its series Handbook of Social Choice and Welfare with number 1-06.
    Handle: RePEc:eee:socchp:1-06
    Contact details of provider: Web page: http://www.elsevier.com/wps/find/bookseriesdescription.cws_home/BS_HE/description

    References listed on IDEAS
    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.:

    as in new window
    1. Eric Friedman & Moulin, Herve, 1995. "Three Methods to Share Joint Costs or Surplus," Working Papers 95-38, Duke University, Department of Economics.
    2. 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.
    3. Téjédo, Cyril & Truchon, Michel, 1999. "Multi-Product Serial Cost Sharing: an Incompatibility Result," Cahiers de recherche 9919, Université Laval - Département d'économique.
    4. SPRUMONT, Yves, 1999. "Coherent Cost-Sharing Rules," Cahiers de recherche 9902, Universite de Montreal, Departement de sciences economiques.
    5. Maurice Koster, 2007. "The Moulin–Shenker rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 271-293, September.
    6. Volij, Oscar & Dagan, Nir, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," Staff General Research Papers 5141, Iowa State University, Department of Economics.
    7. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 229-46, March.
    8. Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 381-413.
    9. Moulin, HervÈ & Shenker, Scott, 1997. "Distributive and Additive Costsharing of an Homogeneous Good," Working Papers 97-21, Duke University, Department of Economics.
    10. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
    11. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    12. E. Loehman & A. Whinston, 1974. "An Axiomatic Approach to Cost Allocation for Public Investment," Public Finance Review, , vol. 2(2), pages 236-250, April.
    13. Thomson, W., 1991. "Resource-Monotonic Solutions to the Problem of Fair Divosion when Preferences are Single-Peaked ," RCER Working Papers 301, University of Rochester - Center for Economic Research (RCER).
    14. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    15. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    16. 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.
    17. Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    18. Tijs, S.H. & Koster, M.A.L., 1998. "General aggregation of demand and cost sharing methods," Other publications TiSEM 43bb1596-ff5b-4567-a25f-9, Tilburg University, School of Economics and Management.
    19. Hougaard, Jens Leth & Thorlund-Petersen, Lars, 2001. "Mixed serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 51-68, January.
    20. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    21. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
    22. 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.
    23. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    24. 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.
    25. Koster, M.A.L., 1998. "Multi-Service Serial Cost Sharing : An Incompatibility with Smoothness," Discussion Paper 1998-122, Tilburg University, Center for Economic Research.
    26. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
    27. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    28. Nir Dagan, 1996. "New Characterizations of Old Bankruptcy Rules," Economic theory and game theory 002, Nir Dagan.
    29. 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.
    30. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
    31. 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.
    32. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
    33. 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.
    34. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer;Society for Economic Design, vol. 4(3), pages 255-272.
    35. Khmelnitskaya, Anna B., 1999. "Marginalist and efficient values for TU games," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 45-54, July.
    36. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    37. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
    38. Young, H Peyton, 1985. "Producer Incentives in Cost Allocation," Econometrica, Econometric Society, vol. 53(4), pages 757-65, July.
    39. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    40. 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.
    41. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    42. YunTong Wang, 2003. "Simple random order methods to share costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 295-314, December.
    43. 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.
    44. William W. Sharkey & Richard P. McLean, 1998. "Weighted Aumann-Shapley pricing," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 511-523.
    45. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    46. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
    47. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:socchp:1-06. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.