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A discussion of the consistency axiom in cost-allocation problems

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Author Info
Justin Leroux () (IEA, HEC Montréal)

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Abstract

The recent literature on cost allocation lacks consensus on what is an appropriate definition of the consistency axiom. We take this as evidence that a careful reexamination is necessary. The starting point of our critique is the widely adopted definition proposed in Moulin and Shenker (1994), which we show to be conceptually flawed. Rectifying this flaw leads to a definition of consistency which already appeared in the recent literature though without satisfactory conceptual justification. We offer a classification of the existing definitions of the consistency axiom by relating them to the definitions of consistency in cooperative games suggested in Davis and Maschler (1965) and Hart and Mas-Colell (1989). We argue that only the latter leads to a meaningful interpretation of consistency when production externalities are present.

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Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number 06-13.

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Length: 14 pages
Date of creation: Nov 2006
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Handle: RePEc:iea:carech:0613

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Postal: Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7
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  1. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February. [Downloadable!] (restricted)
  2. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer, vol. 24(4), pages 373-97.
  3. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September. [Downloadable!] (restricted)
  4. Tijs, S. & Koster, M., 1996. "General aggregation of demand and cost sharing methods," Discussion Paper 87, Tilburg University, Center for Economic Research. [Downloadable!]
  5. 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)
  6. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
  7. Marc Fleurbaey & Francois Maniquet, 1999. "Cooperative production with unequal skills: The solidarity approach to compensation," Social Choice and Welfare, Springer, vol. 16(4), pages 569-583. [Downloadable!] (restricted)
  8. Ehlers,Lars & Klaus,Bettina, 2005. "Consistent House Allocation," Research Memoranda 007, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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  9. Albizuri, M. Josune & Zarzuelo, Jose M., 2007. "The dual serial cost-sharing rule," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 150-163, March. [Downloadable!] (restricted)
  10. Lensberg, Terje, 1987. "Stability and Collective Rationality," Econometrica, Econometric Society, vol. 55(4), pages 935-61, July. [Downloadable!] (restricted)
  11. Eric J. Friedman, 2004. "Paths and consistency in additive cost sharing," International Journal of Game Theory, Springer, vol. 32(4), pages 501-518, 08. [Downloadable!] (restricted)
  12. Thomson, William & Zhou, Lin, 1993. "Consistent Solutions in Atomless Economies," Econometrica, Econometric Society, vol. 61(3), pages 575-87, May. [Downloadable!] (restricted)
  13. Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April. [Downloadable!] (restricted)
  14. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November. [Downloadable!] (restricted)
  15. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357 Elsevier. [Downloadable!] (restricted)
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  16. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-67, November. [Downloadable!] (restricted)
  17. 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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