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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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  1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June. [Downloadable!] (restricted)
  2. 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)
  3. 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)
  4. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272. [Downloadable!] (restricted)
  5. Young, H Peyton, 1985. "Producer Incentives in Cost Allocation," Econometrica, Econometric Society, vol. 53(4), pages 757-65, July. [Downloadable!] (restricted)
  6. 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)
  7. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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  9. 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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  10. 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)
  11. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  12. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November. [Downloadable!] (restricted)
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  13. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July. [Downloadable!] (restricted)
  14. 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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  15. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September. [Downloadable!] (restricted)
  16. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September. [Downloadable!] (restricted)
  17. Tijs, S. & Koster, M., 1996. "General aggregation of demand and cost sharing methods," Discussion Paper 87, Tilburg University, Center for Economic Research. [Downloadable!]
  18. 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)
  19. 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.
    Other versions:
  20. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  21. Sprumont, Yves, 2000. "Coherent Cost-Sharing Rules," Games and Economic Behavior, Elsevier, vol. 33(1), pages 126-144, October. [Downloadable!] (restricted)
  22. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August. [Downloadable!] (restricted)
  23. 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).
  24. Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer, vol. 19(2), pages 381-413. [Downloadable!] (restricted)
    Other versions:
  25. William W. Sharkey & Richard P. McLean, 1998. "Weighted Aumann-Shapley pricing," International Journal of Game Theory, Springer, vol. 27(4), pages 511-523. [Downloadable!] (restricted)
  26. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  27. 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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  28. Maurice Koster, 2007. "The Moulin–Shenker rule," Social Choice and Welfare, Springer, vol. 29(2), pages 271-293, September. [Downloadable!] (restricted)
  29. Koster, M., 1998. "Multi-service serial cost sharing : an incompatibility with smoothness," Discussion Paper 122, Tilburg University, Center for Economic Research. [Downloadable!]
  30. 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)
  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. [Downloadable!] (restricted)
  32. 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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  33. Laffont, J. J. & Moulin, H., 1982. "Introduction," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 1-3, June. [Downloadable!] (restricted)
  34. 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)
    Other versions:
  35. 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)
  36. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April. [Downloadable!] (restricted)
  37. Khmelnitskaya, Anna B., 1999. "Marginalist and efficient values for TU games," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 45-54, July. [Downloadable!] (restricted)
  38. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics. [Downloadable!]
  39. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
  40. 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)
  41. Hougaard, Jens Leth & Thorlund-Petersen, Lars, 2001. "Mixed serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 51-68, January. [Downloadable!] (restricted)
  42. Martin Shubik, 1961. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Cowles Foundation Discussion Papers 112, Cowles Foundation, Yale University. [Downloadable!]
  43. 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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