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Bargaining, coalitions and externalities: A comment on Maskin

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

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Abstract

We first observe that two of Maskin's results do not extend beyond three players: we construct a four-player partition function with non-positive externalities whose unique solution is inefficient, as well as a four-player characteristic function that has a unique efficient solution for each ordering of the players, but for which the payoff vector obtained by averaging these solutions over the different orderings does not coincide with the Shapley value. On the other hand, we reinforce Maskins insight that externalities may play a crucial role in generating inefficiency. Many existing solutions on how to share profits assume or derive the property of efficiency. Yet we argue that players may have an interest to choose with whom to bargain. We illustrate how this may trigger inefficiency, especially in the presence of externalities, even if bargaining among any group of agents results in an efficient distribution of the surplus they can produce. We also provide some sufficient conditions for efficiency.

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Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2008-11.

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Date of creation: 20 Nov 2008
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Handle: RePEc:imd:wpaper:wp2008-11

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Related research
Keywords: externalities; coalition formation; Shapley value;

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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

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  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. 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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  8. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November. [Downloadable!] (restricted)
  9. Geoffroy de Clippel & Roberto Serrano, 2007. "Marginal contributions and externalities in the value," Working Papers 2007-04, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales. [Downloadable!]
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  10. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2006. "Efficient bidding with externalities," Games and Economic Behavior, Elsevier, vol. 57(2), pages 304-320, November. [Downloadable!] (restricted)
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  11. Montero, M., 1999. "Coalition formation in games with externalities," Discussion Paper 121, Tilburg University, Center for Economic Research. [Downloadable!]
  12. Bloch, Francis, 2002. "Coalitions and Networks in Industrial Organization," Manchester School, University of Manchester, vol. 70(1), pages 36-55, January. [Downloadable!] (restricted)
  13. 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)
  14. 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)
  15. 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)
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