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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
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Kimya, Mert, 2020. "Equilibrium coalitional behavior," Theoretical Economics, Econometric Society, vol. 15(2), May.
    2. 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.
    3. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. 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.
    5. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    6. 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.
    7. Toshiyuki Hirai, 2018. "Single-payoff farsighted stable sets in strategic games with dominant punishment strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1087-1111, November.
    8. Kawasaki, Ryo, 2015. "Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 8-12.
    9. 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.
    10. Shino, Junnosuke & Kawasaki, Ryo, 2012. "Farsighted stable sets in Hotelling’s location games," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 23-30.
    11. Aivazian, Varouj A. & Callen, Jeffrey L., 2023. "The Coase Theorem and the empty core: Inspecting the entrails after four decades," International Review of Law and Economics, Elsevier, vol. 73(C).
    12. Talamàs, Eduard, 2018. "Fair stable sets of simple games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 574-584.
    13. Kawasaki, Ryo & Sato, Takashi & Muto, Shigeo, 2015. "Farsightedly stable tariffs," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 118-124.

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    More about this item

    Keywords

    Cooperative games; Farsighted core; Consistent set; von Neumann–Morgenstern farsighted stable set; Shapley value Cooperative games; Shapley value;
    All these keywords.

    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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