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On the number of blocks required to access the core

Author

Listed:
  • Sylvain Béal

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Éric Rémila

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, LIP - Laboratoire de l'Informatique du Parallélisme - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - Inria - Institut National de Recherche en Informatique et en Automatique - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

For any transferable utility game in coalitional form with nonempty core, we show that the number of blocks required to switch from an imputation out of the core to a core imputation is less than or equal to n(n−1)/2, where n is the number of players. This number considerably improves the bounds found by Kóczy (2006) [5] and Yang (2010) [11]. Our result relies on an altered version of the procedure proposed by Sengupta and Sengupta (1996) [9]. The use of the Davis-Maschler reduced-games is also pointed out.

Suggested Citation

  • Sylvain Béal & Éric Rémila & Philippe Solal, 2012. "On the number of blocks required to access the core," Post-Print halshs-00662489, HAL.
    • Handle: RePEc:hal:journl:halshs-00662489
    DOI: 10.1016/j.dam.2011.12.022
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    References listed on IDEAS

    as
    1. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
    2. Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2008. "Farsighted coalitional stability in TU-games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 303-313, November.
    3. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
    4. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    5. Koczy, Laszlo A., 2006. "The core can be accessed with a bounded number of blocks," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 56-64, December.
    6. 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.
    7. 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).
    8. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    9. Manea, Mihai, 2007. "Core tatonnement," Journal of Economic Theory, Elsevier, vol. 133(1), pages 331-349, March.
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    Citations

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    Cited by:

    1. Yang, Yi-You, 2012. "On the accessibility of core-extensions," Games and Economic Behavior, Elsevier, vol. 74(2), pages 687-698.
    2. Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.
    3. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2013. "An optimal bound to access the core in TU-games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 1-9.
    4. Péter Biró & Gethin Norman, 2013. "Analysis of stochastic matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 1021-1040, November.
    5. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    6. Yi-You Yang, 2020. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 89(4), pages 453-469, November.
    7. Herings, P. Jean-Jacques & Kóczy, László Á., 2021. "The equivalence of the minimal dominant set and the myopic stable set for coalition function form games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 67-79.
    8. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2011. "On the number of blocks required to access the coalition structure core," MPRA Paper 29755, University Library of Munich, Germany.
    9. Péter Szikora, 2013. "Introduction into the literature of cooperative game theory with special emphasis on dynamic games and the core," Proceedings- 11th International Conference on Mangement, Enterprise and Benchmarking (MEB 2013),, Óbuda University, Keleti Faculty of Business and Management.
    10. 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.
    11. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    12. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.

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    More about this item

    Keywords

    Core; Excess function; Dominance path; Davis-Maschler reduced-game;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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