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Farsighted coalitional stability in TU-games

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  • Béal, Sylvain
  • Durieu, Jacques
  • Solal, Philippe

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

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References

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  1. Xue, Licun, 1997. "Nonemptiness of the Largest Consistent Set," Journal of Economic Theory, Elsevier, vol. 73(2), pages 453-459, April.
  2. Page Jr, Frank H & Wooders, Myrna H & Kamat, Samir, 2001. "Networks And Farsighted Stability," The Warwick Economics Research Paper Series (TWERPS) 621, University of Warwick, Department of Economics.
  3. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer, vol. 11(3), pages 603-627.
  4. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2006. "Convex games versus clan games," Working Papers 381, Bielefeld University, Center for Mathematical Economics.
  5. Effrosyni Diamantoudi & Licun Xue, 2006. "Lucas Counter Example Revisited," Departmental Working Papers 2005-09, McGill University, Department of Economics.
  6. Effrosyni Diamantoudi & Licun Xue, . "Farsighted Stability in Hedonic Games," Economics Working Papers 2000-12, School of Economics and Management, University of Aarhus.
  7. Akihiro Suzuki & Shigeo Muto, 2005. "Farsighted Stability in an n-Person Prisoner’s Dilemma," International Journal of Game Theory, Springer, vol. 33(3), pages 431-445, 09.
  8. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
  9. Masuda, Takeshi, 2002. "Farsighted stability in average return games," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 169-181, November.
  10. MAULEON, Ana & VANNETELBOSCH, Vincent, . "Farsightedness and cautiousness in coalition formation games with positive spillovers," CORE Discussion Papers RP -1729, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
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Cited by:
  1. Junnosuke Shino, 2008. "Farsighted Stable Sets in Hotelling's Location Games," Departmental Working Papers 200808, Rutgers University, Department of Economics.
  2. Debraj Ray & Rajiv Vohra, 2013. "The Farsighted Stable Set," Working Papers 2013-11, Brown University, Department of Economics.
  3. Xiaozhou Xu & Shenle Pan & Eric Ballot, 2012. "Allocation of Transportation Cost & CO2 Emission in Pooled Supply Chains Using Cooperative Game Theory," Post-Print hal-00733491, HAL.
  4. Anindya Bhattacharya & Victoria Brosi, 2011. "An existence result for farsighted stable sets of games in characteristic function form," International Journal of Game Theory, Springer, vol. 40(2), pages 393-401, May.
  5. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers 2013-1, Brown University, Department of Economics.
  6. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "On the number of blocks required to access the core," MPRA Paper 26578, University Library of Munich, Germany.

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