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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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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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References

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  1. Montero, M.P., 1999. "Coalition Formation in Games with Externalities," Discussion Paper, Tilburg University, Center for Economic Research 1999-121, Tilburg University, Center for Economic Research.
  2. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, Econometric Society, vol. 51(4), pages 1047-64, July.
  3. Bloch, Francis, 2002. "Coalitions and Networks in Industrial Organization," Manchester School, University of Manchester, University of Manchester, vol. 70(1), pages 36-55, January.
  4. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  5. Debraj Ray & Rajiv Vohra, 2001. "Coalitional Power and Public Goods," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 109(6), pages 1355-1384, December.
  6. Inés Macho & David Pérez-Castrillo & David Wettstein, 2005. "Efficient Bidding with Externalitites," Working Papers 159, Barcelona Graduate School of Economics.
  7. Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions And Externalities In The Value," Economics Working Papers we057339, Universidad Carlos III, Departamento de Economía.
  8. Debraj Ray & Rajiv Vohra, 1998. "A Theory of Endogenous Coalition Structures," Working Papers, Brown University, Department of Economics 98-1, Brown University, Department of Economics, revised Jan 1998.
  9. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics, Boston College Department of Economics 449, Boston College Department of Economics.
  10. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, Elsevier, vol. 61(2), pages 242-258, November.
  11. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 90-123, May.
  12. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 38(2), pages 201-230, February.
  13. David Pérez-Castrillo & David Wettstein, . "Bidding For The Surplus: A Non-Cooperative Approach To The Shapley Value," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 461.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  14. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
  15. 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, Elsevier, vol. 135(1), pages 339-356, July.
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Cited by:
  1. Peter J. Wood, 2010. "Climate Change and Game Theory: A Mathematical Survey," CCEP Working Papers, Centre for Climate Economics & Policy, Crawford School of Public Policy, The Australian National University 0210, Centre for Climate Economics & Policy, Crawford School of Public Policy, The Australian National University.
  2. Manfred Kerber & Colin Rowat, 2012. "Sufficient Conditions for the Unique Stable Sets in Three Agent Pillage Games," Discussion Papers, Department of Economics, University of Birmingham 12-11, Department of Economics, University of Birmingham.
  3. Peter Wood, 2010. "Climate Change and Game Theory," Environmental Economics Research Hub Research Reports, Environmental Economics Research Hub, Crawford School of Public Policy, The Australian National University 1062, Environmental Economics Research Hub, Crawford School of Public Policy, The Australian National University.
  4. 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, Toulouse School of Economics (TSE) 12-295, Toulouse School of Economics (TSE).
  5. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers, Brown University, Department of Economics 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," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 710, Institut d'Économie Industrielle (IDEI), Toulouse.

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