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Serial Cost Sharing in Multidimensional Contexts (May 2002 revised version)

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  • Cyril Téjédo
  • Michel Truchon

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Abstract

The Serial Cost Sharing Rule was originally conceived for situations where the demands of agents pertain to a homogeneous private good, produced by an unreplicable technology. In this context, it is endowed with a variety of desirable equity and coherency properties. This paper investigates the extension of this rule to the context where agents request many goods that may be public, private or specific to some of them, where the aggregation rule may be very general and where demands may have to be scaled in a non proportional way, more precisely along paths, in order to compute cost shares. It proposes the Path Serial Rule to address these general problems and explores some of its properties and characteristics. Some of them are transposed directly from the single good context to the general one. However, it is shown that in the general context, the serial principle is incompatible with the basic equal treatment of equals. Thus, it is weakened by requiring that it holds only on the paths along which demands must be scaled when needed. The resulting weaker Path Serial Principle characterizes the Path Serial Rule together with the Equal Treatment of Equivalent Demands, a stronger form of Equal Treatment of Equals. La règle de partage séquentiel des coûts a été conçue à l origine pour le cas où les demandes des agents portent sur un bien privé homogène, produit par une technologie non reproductible. Dans un tel contexte, cette règle satisfait de nombreuses propriétés d équité et de cohérence. Dans cet article, on étudie l extension de cette règle aux cas où les demandes des agents peuvent être des vecteurs qui ne représentent pas forcément des biens homogènes entre les agents, dont l agrégation ne se fait pas uniquement via la sommation et où les demandes doivent être ajustées de manière non proportionnelle, plus précisément le long d un sentier, pour le calcul des parts de coût. On explore ensuite certaines propriétés et caractéristiques de cette règle plus générale. Certaines sont transposées directement du contexte à un seul bien au contexte général. Cependant, on montre que le principe séquentiel est, dans ce contexte général, incompatible avec l incontournable traitement égalitaire des égaux. Il faut donc l affaiblir et plus précisément exiger qu il soit respecté uniquement le long des sentiers servant à ajuster les demandes le cas échéant. Cette forme affaiblie de principe séquentiel, combinée à une forme plus forte de traitement égalitaire des égaux, caractérise la règle proposée dans cet article.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2001s-68.

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Date of creation: 01 Dec 2001
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Handle: RePEc:cir:cirwor:2001s-68

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Keywords: Serial cost sharing; multi products; general aggregation; Partage séquentiel des coûts; multi-produits; agrégation générale;

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References

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  1. Cyril Téjédo & Michel Truchon, 2002. "Monotonicity and Bounds for Cost Shares under the Path Serial Rule," Cahiers de recherche 02-05, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
  2. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  3. Sprumont, Y., 1996. "Ordinal Cost Sharing," Cahiers de recherche 9624, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. 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.
  5. Moulin, Herve, 1995. "Cost-Sharing under Increasing Returns: A Comparisonof Simple Mechanisms," Working Papers 95-19, Duke University, Department of Economics.
  6. 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.
  7. 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.
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