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A discussion of the consistency axiom in cost-allocation problems

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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
Date of revision:
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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Postal: Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7
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  1. Eric J. Friedman, 2004. "Paths and consistency in additive cost sharing," International Journal of Game Theory, Springer, vol. 32(4), pages 501-518, 08.
  2. Ehlers,Lars & Klaus,Bettina, 2005. "Consistent House Allocation," Research Memorandum 007, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Thomson, William & Zhou, Lin, 1993. "Consistent Solutions in Atomless Economies," Econometrica, Econometric Society, vol. 61(3), pages 575-87, May.
  4. Tijs, S.H. & Koster, M.A.L., 1996. "General Aggregation of Demand and Cost Sharing Methods," Discussion Paper 1996-87, Tilburg University, Center for Economic Research.
  5. 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.
  6. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  7. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
  8. 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.
  9. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  10. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November.
  11. Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
  12. 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.
  13. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-67, November.
  14. Lensberg, Terje, 1987. "Stability and Collective Rationality," Econometrica, Econometric Society, vol. 55(4), pages 935-61, July.
  15. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  16. Albizuri, M. Josune & Zarzuelo, Jose M., 2007. "The dual serial cost-sharing rule," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 150-163, March.
  17. repec:cup:cbooks:9780521343831 is not listed on IDEAS
  18. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer, vol. 24(4), pages 373-97.
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