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Paths and consistency in additive cost sharing

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  • Eric J. Friedman

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    Abstract

    We provide a direct proof of a representation theorem for additive cost sharing methods as sums of path methods. Also, by directly considering the paths that generate some common additive cost sharing methods (Aumann-Shapley, Shapley Shubik, and Serial Cost) we show that they are consistent. These results follow directly from a simple sufficient condition for consistency: being generated by an associative path. We also introduce a new axiom, dummy consistency, which is quite mild. Using this, we also show that the Aumann-Shapley and Serial Cost methods are the unique (additive) consistent extension of their restriction on all two agent problems, while the Shapley-Shubik method has multiple consistent extensions but a unique anonymous scale invariant one. Copyright Springer-Verlag 2004

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    File URL: http://hdl.handle.net/10.1007/s001820400173
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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Games Theory.

    Volume (Year): 32 (2004)
    Issue (Month): 4 (08)
    Pages: 501-518

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    Handle: RePEc:spr:jogath:v:32:y:2004:i:4:p:501-518

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    Web page: http://link.springer.de/link/service/journals/00182/index.htm

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    Cited by:
    1. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer, vol. 31(4), pages 693-707, December.
    2. SPRUMONT, Yves, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Cahiers de recherche 01-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. SPRUMONT, Yves, 2004. "Nearly Serial Sharing Methods," Cahiers de recherche 17-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Mariusz Kaleta & Eugeniusz Toczylowski, 2009. "A cost allocation framework for lp and glp games," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 27-46.
    5. Maurice Koster, 2007. "The Moulin–Shenker rule," Social Choice and Welfare, Springer, vol. 29(2), pages 271-293, September.
    6. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer, vol. 42(2), pages 439-460, May.
    7. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
    8. Friedman, Eric J., 2012. "Asymmetric Cost Sharing mechanisms," Games and Economic Behavior, Elsevier, vol. 75(1), pages 139-151.
    9. SPRUMONT, Yves & MOULIN, Hervé, 2005. "Fair Allocation of Production Externalities: Recent Results," Cahiers de recherche 2005-22, Universite de Montreal, Departement de sciences economiques.
    10. Albizuri, M. Josune & Zarzuelo, Jose M., 2007. "The dual serial cost-sharing rule," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 150-163, March.
    11. Justin Leroux, 2006. "A discussion of the consistency axiom in cost-allocation problems," Cahiers de recherche 06-13, HEC Montréal, Institut d'économie appliquée.

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