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Farsighted Coalitional Stability in TU-games

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  • Béal, Sylvain

    ()
    (Sonderforschungsbereich 504)

  • Durieu, Jacques

    (CREUSET, University of Saint-Etienne)

  • Solal, Philippe

    (CREUSET, University of Saint-Etienne)

Abstract

We study farsighted coalitional stability in the context of TUgames. Chwe (1994, p.318) notes that, in this context, it is difficult to prove nonemptiness of the largest consistent set. We show that every TU-game has a nonempty largest consistent set. Moreover, the proof of this result points out that each TU-game has a farsighted stable set. We go further by providing a characterization of the collection of farsighted stable sets in TU-games. We also show that the farsighted core of a TU-game is empty or is equal to the set of imputations of the game. Next, the relationships between the core and the largest consistent set are studied in superadditive TU-games and in clan games. In the last section, we explore the stability of the Shapley value. It is proved that the Shapley value of a superadditive TU-game is always a stable imputation: it is a core imputation or it constitutes a farsighted stable set. A necessary and sufficient condition for a superadditive TU-game to have the Shapley value in the largest consistent set is given.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 07-57.

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Length: 40 pages
Date of creation: 06 Aug 2007
Date of revision:
Handle: RePEc:xrs:sfbmaa:07-57

Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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References

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  1. Effrosyni Diamantoudi & Licun Xue, 2006. "Lucas Counter Example Revisited," Departmental Working Papers 2005-09, McGill University, Department of Economics.
  2. Frank H. Page Jr. & Myrna H. Wooders & Samir Kamat, 2002. "Networks and Farsighted Stability," Computing in Economics and Finance 2002 370, Society for Computational Economics.
  3. Xue, Licun, 1997. "Nonemptiness of the Largest Consistent Set," Journal of Economic Theory, Elsevier, vol. 73(2), pages 453-459, April.
  4. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
  5. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer, vol. 11(3), pages 603-627.
  6. 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).
  7. 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.
  8. Masuda, Takeshi, 2002. "Farsighted stability in average return games," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 169-181, November.
  9. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer, vol. 21(1), pages 39-61, 08.
  10. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2006. "Convex Games versus Clan Games," Discussion Paper 2006-58, Tilburg University, Center for Economic Research.
  11. 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.
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Cited by:
  1. 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.
  2. 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.
  3. Shino, Junnosuke & Kawasaki, Ryo, 2012. "Farsighted stable sets in Hotelling’s location games," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 23-30.
  4. Debraj Ray & Rajiv Vohra, 2013. "The Farsighted Stable Set," Working Papers 2013-11, Brown University, Department of Economics.
  5. 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.
  6. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers 2013-1, Brown University, Department of Economics.

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