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Paths and consistency in additive cost sharing

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  • Eric J. Friedman

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

Suggested Citation

  • Eric J. Friedman, 2004. "Paths and consistency in additive cost sharing," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 501-518, August.
    • Handle: RePEc:spr:jogath:v:32:y:2004:i:4:p:501-518
    DOI: 10.1007/s001820400173
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    Cited by:

    1. EHLERS, Lars & WESTKAMP, Alexander, 2011. "Strategy-Proof Tie-Breaking," Cahiers de recherche 2011-07, Universite de Montreal, Departement de sciences economiques.
    2. Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 155-184, June.
    3. Justin Leroux, 2006. "A discussion of the consistency axiom in cost-allocation problems," Cahiers de recherche 06-13, HEC Montréal, Institut d'économie appliquée.
    4. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 709-710, December.
    5. Yves Sprumont, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Econometrica, Econometric Society, vol. 78(5), pages 1711-1748, September.
    6. Friedman, Eric J., 2012. "Asymmetric Cost Sharing mechanisms," Games and Economic Behavior, Elsevier, vol. 75(1), pages 139-151.
    7. Bergantiños, Gustavo & Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2016. "Consistency in PERT problems," MPRA Paper 68973, University Library of Munich, Germany.
    8. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    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.
    10. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 439-460, May.
    11. Maurice Koster, 2007. "The Moulin–Shenker rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 271-293, September.
    12. 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.
    13. Mariusz Kaleta & Eugeniusz Toczyłowski, 2009. "A cost allocation framework for LP and GLP games," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(4), pages 27-46.
    14. Eric Bahel & Christian Trudeau, 2014. "Shapley–Shubik methods in cost sharing problems with technological cooperation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 261-285, August.
    15. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.

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