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Farsighted coalitional stability in TU-games

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Author Info
Béal, Sylvain
Durieu, Jacques
Solal, Philippe

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Abstract

We study farsighted coalitional stability in the context of TU-games. We show that every TU-game has a nonempty largest consistent set and that each TU-game has a von Neumann-Morgenstern farsighted stable set. We characterize the collection of von Neumann-Morgenstern farsighted stable sets. We also show that the farsighted core is either empty or equal to the set of imputations of the game. In the last section, we explore the stability of the Shapley value. The Shapley value of a superadditive game is a stable imputation: it is a core imputation or it constitutes a von Neumann-Morgenstern farsighted stable set. A necessary and sufficient condition for a superadditive game to have the Shapley value in the largest consistent set is given.

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File URL: http://www.sciencedirect.com/science/article/B6V88-4SR711X-1/2/f5458bb338b9fe51e86ab1eb230dd2d2
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Publisher Info
Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 56 (2008)
Issue (Month): 3 (November)
Pages: 303-313
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Handle: RePEc:eee:matsoc:v:56:y:2008:i:3:p:303-313

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Web page: http://www.elsevier.com/locate/inca/505565

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Related research
Keywords: Cooperative games Farsighted core Consistent set von Neumann-Morgenstern farsighted stable set Shapley value;

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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. Ana Mauleon & Vincent Vannetelbosch, 2004. "Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers," Theory and Decision, Springer, vol. 56(3), pages 291-324, 05. [Downloadable!]
  2. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August. [Downloadable!] (restricted)
  3. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2006. "Convex games versus clan games," Discussion Paper 58, Tilburg University, Center for Economic Research. [Downloadable!]
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  4. Effrosyni Diamantoudi & Licun Xue, 2006. "Lucas Counter Example Revisited," Departmental Working Papers 2005-09, McGill University, Department of Economics. [Downloadable!]
  5. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer, vol. 11(3), pages 603-627. [Downloadable!] (restricted)
  6. Xue, Licun, 1997. "Nonemptiness of the Largest Consistent Set," Journal of Economic Theory, Elsevier, vol. 73(2), pages 453-459, April. [Downloadable!] (restricted)
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