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Marginal contributions and externalities in the value

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Author Info
Geoffroy de Clippel () (Brown University)
Roberto Serrano () (Brown University and IMDEA Social Sciences)

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Abstract

Our concern is the extension of the theory of the Shapley value to games with externalities. Using the standard axiom systems behind the Shapley value for an arbitrary exogenous coalition structure leads to the identification of bounds on players’ payoffs around an \"externality-free\" value. In endogenizing the coalition structure, we analyze a two-stage process of coalition formation in whose second stage our axiomatic results are applied. We find reasons to explain inefficient coalition structures, and provide sufficient conditions for efficiency.

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Publisher Info
Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2007-04.

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Date of creation: 28 Feb 2007
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Publication status: Published in Econometrica 76(6), November 2008: 1413-1436
Handle: RePEc:imd:wpaper:wp2007-04

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Related research
Keywords: externalities; marginal contributions; Shapley value; Pigouvian transfers; coalition formation;

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D62 - Microeconomics - - Welfare Economics - - - Externalities

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153. [Downloadable!] (restricted)
    Other versions:
  2. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July. [Downloadable!] (restricted)
  3. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, vol. 26(2), pages 286-336, January. [Downloadable!] (restricted)
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  4. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March. [Downloadable!] (restricted)
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  5. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December. [Downloadable!] (restricted)
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  6. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July. [Downloadable!] (restricted)
  7. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation, Yale University. [Downloadable!]
  8. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October. [Downloadable!] (restricted)
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  9. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation, Yale University. [Downloadable!]
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  10. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72. [Downloadable!] (restricted)
  11. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer, vol. 18(1), pages 37-44.
  12. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2005. "Efficient Bidding with Externalities," UFAE and IAE Working Papers 641.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
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  13. Montero, M., 1999. "Coalition formation in games with externalities," Discussion Paper 121, Tilburg University, Center for Economic Research. [Downloadable!]
  14. Bloch, Francis, 2002. "Coalitions and Networks in Industrial Organization," Manchester School, University of Manchester, vol. 70(1), pages 36-55, January. [Downloadable!] (restricted)
  15. Pham Do, K.H. & Norde, H., 2002. "The Shapley value for partition function form games," Discussion Paper 4, Tilburg University, Center for Economic Research. [Downloadable!]
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  16. Roger B. Myerson, 1976. "Value of Games in Partition Function Form," Discussion Papers 244, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  17. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  18. Debraj Ray & Rajiv Vohra, 2001. "Coalitional Power and Public Goods," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1355-1384, December. [Downloadable!] (restricted)
  19. Khmelnitskaya, Anna B., 1999. "Marginalist and efficient values for TU games," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 45-54, July. [Downloadable!] (restricted)
  20. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February. [Downloadable!] (restricted)
  21. repec:fth:tilbur:99121 is not listed on IDEAS
  22. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May. [Downloadable!] (restricted)
  23. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Bhaskar Dutta & Lars Ehlers & Anirban Kar, 2008. "Externalities, Potential, Value And Consistency," Working papers 168, Centre for Development Economics, Delhi School of Economics. [Downloadable!]
    Other versions:
  2. Ambec, S. & Ehlers, L., 2006. "Sharing a river among satiable countries," Working Papers 200605, Grenoble Applied Economics Laboratory (GAEL). [Downloadable!]
    Other versions:
  3. Sergiu Hart & Andreu Mas-Colell, 2008. "Cooperative Games in Strategic Form," Levine's Working Paper Archive 122247000000002406, David K. Levine. [Downloadable!]
    Other versions:
  4. McQuillin, Ben, 2008. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," MPRA Paper 12049, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  5. Geoffroy de Clippel & Roberto Serrano, 2008. "Bargaining, Coalitions and Externalities: a Comment on Maskin," Working Papers 2008-16, Brown University, Department of Economics. [Downloadable!]
    Other versions:
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