IDEAS home Printed from https://ideas.repec.org/p/hal/journl/ujm-00176491.html
   My bibliography  Save this paper

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 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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Sylvain Béal & Jacques Durieu & Philippe Solal, 2007. "Farsighted Coalitional Stability in TU-Games," Post-Print ujm-00176491, HAL.
    • Handle: RePEc:hal:journl:ujm-00176491
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
    3. Effrosyni Diamantoudi & Licun Xue, 2006. "Lucas Counter Example Revisited," Departmental Working Papers 2005-09, McGill University, Department of Economics.
    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. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Page, Frank H., Jr. & Wooders, Myrna H., 2005. "Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games," Economic Research Papers 269618, University of Warwick - Department of Economics.
    12. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Masuda, Takeshi, 2002. "Farsighted stability in average return games," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 169-181, November.
    14. Xue, Licun, 1997. "Nonemptiness of the Largest Consistent Set," Journal of Economic Theory, Elsevier, vol. 73(2), pages 453-459, April.
    15. A Bhattacharya, "undated". "Stable and Efficient Networks with Farsighted Players: the Largest Consistent Set," Discussion Papers 09/34, Department of Economics, University of York.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kimya, Mert, 2020. "Equilibrium coalitional behavior," Theoretical Economics, Econometric Society, vol. 15(2), May.
    2. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 202106, University of Sydney, School of Economics.
    3. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
    4. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2021. "Implementation in largest consistent set via rights structures," Games and Economic Behavior, Elsevier, vol. 128(C), pages 202-212.
    5. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2019. "Implementation with foresighted agents," MPRA Paper 102496, University Library of Munich, Germany.
    6. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Kimya, Mert, 2021. "Coalition Formation Under Dominance Invariance," Working Papers 2021-06, University of Sydney, School of Economics.
    8. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    9. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    10. Ana Mauleon & Elena Molis & Vincent Vannetelbosch & Wouter Vergote, 2014. "Dominance invariant one-to-one matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 925-943, November.
    11. Mert Kimya, 2023. "Coalition Formation Under Dominance Invariance," Dynamic Games and Applications, Springer, vol. 13(2), pages 480-496, June.
    12. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2009. "Farsightedly stable networks," Games and Economic Behavior, Elsevier, vol. 67(2), pages 526-541, November.
    13. Hannu Vartiainen, 2007. "Dynamic Farsighted Stability," Discussion Papers 22, Aboa Centre for Economics.
    14. Bloch, Francis & van den Nouweland, Anne, 2020. "Farsighted stability with heterogeneous expectations," Games and Economic Behavior, Elsevier, vol. 121(C), pages 32-54.
    15. Shino, Junnosuke & Kawasaki, Ryo, 2012. "Farsighted stable sets in Hotelling’s location games," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 23-30.
    16. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2023. "Social Rationalizability with Mediation," Dynamic Games and Applications, Springer, vol. 13(2), pages 440-461, June.
    17. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2019. "Stability of networks under horizon-K farsightedness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 177-201, July.
    18. Dutta, Bhaskar & Vartiainen, Hannu, 2020. "Coalition formation and history dependence," Theoretical Economics, Econometric Society, vol. 15(1), January.
    19. Bhaskar Dutta & Hannu Vartiainen, 2018. "Coalition Formation and History Dependence," Working Papers 1006, Ashoka University, Department of Economics.
    20. Pierre de Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2024. "Local farsightedness in network formation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 20(2), pages 199-226, June.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:ujm-00176491. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.