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Farsighted Coalitional Stability in TU-games

Author

Listed:
  • Sylvain Béal

    (CREUSET - Centre de Recherche Economique de l'Université de Saint Etienne - UJM - Université Jean Monnet [Saint-Étienne])

  • Jacques Durieu

    (CREUSET - Centre de Recherche Economique de l'Université de Saint Etienne - UJM - Université Jean Monnet [Saint-Étienne])

  • Philippe Solal

    (CREUSET - Centre de Recherche Economique de l'Université de Saint Etienne - UJM - Université Jean Monnet [Saint-Étienne])

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

Suggested Citation

  • Sylvain Béal & Jacques Durieu & Philippe Solal, 2008. "Farsighted Coalitional Stability in TU-games," Post-Print hal-00334049, HAL.
  • Handle: RePEc:hal:journl:hal-00334049
    DOI: 10.1016/j.mathsocsci.2008.06.003
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00334049
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    References listed on IDEAS

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    1. Page, Frank Jr. & Wooders, Myrna H. & Kamat, Samir, 2005. "Networks and farsighted stability," Journal of Economic Theory, Elsevier, vol. 120(2), pages 257-269, February.
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    4. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    5. Akihiro Suzuki & Shigeo Muto, 2005. "Farsighted Stability in an n-Person Prisoner’s Dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 431-445, September.
    6. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 39-61, August.
    7. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Convex Games Versus Clan Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 363-372.
    8. 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, May.
    9. 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.
    10. Masuda, Takeshi, 2002. "Farsighted stability in average return games," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 169-181, November.
    11. Xue, Licun, 1997. "Nonemptiness of the Largest Consistent Set," Journal of Economic Theory, Elsevier, vol. 73(2), pages 453-459, April.
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    Citations

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    Cited by:

    1. 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.
    2. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers 2013-1, 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. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    5. Gedai, Endre & Kóczy, László Á. & Zombori, Zita, 2012. "Cluster games: A novel, game theory-based approach to better understand incentives and stability in clusters," MPRA Paper 65095, University Library of Munich, Germany.
    6. Kawasaki, Ryo, 2015. "Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 8-12.
    7. Anindya Bhattacharya & Victoria Brosi, 2011. "An existence result for farsighted stable sets of games in characteristic function form," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 393-401, May.
    8. Shino, Junnosuke & Kawasaki, Ryo, 2012. "Farsighted stable sets in Hotelling’s location games," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 23-30.
    9. repec:eee:gamebe:v:108:y:2018:i:c:p:574-584 is not listed on IDEAS
    10. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications, Elsevier.
    11. Kawasaki, Ryo & Sato, Takashi & Muto, Shigeo, 2015. "Farsightedly stable tariffs," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 118-124.

    More about this item

    Keywords

    Cooperative games; Farsighted core; Consistent set; von Neumann–Morgenstern farsighted stable set; Shapley value Cooperative games; Shapley value;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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