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Bargaining, Coalitions and Externalities: a Comment on Maskin

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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 nonpositive 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 Maskin’s 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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Bibliographic Info

Paper provided by Brown University, Department of Economics in its series Working Papers with number 2008-16.

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Date of creation: 2008
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Handle: RePEc:bro:econwp:2008-16

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Postal: Department of Economics, Brown University, Providence, RI 02912

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Keywords: externalities; coalition formation; Shapley value;

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  1. Montero, M.P., 1999. "Coalition Formation in Games with Externalities," Discussion Paper 1999-121, Tilburg University, Center for Economic Research.
  2. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  3. Inés Macho & David Pérez-Castrillo & David Wettstein, 2005. "Efficient Bidding with Externalitites," Working Papers 159, Barcelona Graduate School of Economics.
  4. Bloch, Francis, 2002. "Coalitions and Networks in Industrial Organization," Manchester School, University of Manchester, vol. 70(1), pages 36-55, January.
  5. Debraj Ray & Rajiv Vohra, 1996. "A Theory of Endogenous Coalition Structure," Papers 0068, Boston University - Industry Studies Programme.
  6. 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.
  7. Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions and Externalities in the Value," Working Papers 2005-11, Brown University, Department of Economics.
  8. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
  9. 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.
  10. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
  11. 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.
  12. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
  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.
  14. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  15. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
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Cited by:
  1. Wood, Peter John, 2010. "Climate Change and Game Theory," Research Reports 95061, Australian National University, Environmental Economics Research Hub.
  2. Le Breton, Michel & Van Der Straeten, Karine, 2012. "Alliances Electorales entre Deux Tours de Scrutin : Le Point de Vue de la Théorie des Jeux Coopératifs et une Application aux Elections Régionales de Mars 2010," IDEI Working Papers 710, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. Manfred Kerber & Colin Rowat, 2012. "Sufficient Conditions for the Unique Stable Sets in Three Agent Pillage Games," Discussion Papers 12-11, Department of Economics, University of Birmingham.
  4. Peter J. Wood, 2010. "Climate Change and Game Theory: A Mathematical Survey," CCEP Working Papers 0210, Centre for Climate Economics & Policy, Crawford School of Public Policy, The Australian National University.
  5. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers 2013-1, Brown University, Department of Economics.
  6. Le Breton, Michel & Van Der Straeten, Karine, 2012. "Alliances Electorales entre Deux Tours de Scrutin : Le Point de Vue de la Théorie des Jeux Coopératifs et une Application aux Elections Régionales de Mars 2010," TSE Working Papers 12-295, Toulouse School of Economics (TSE).

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