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On the number of blocks required to access the core

Author

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  • Béal, Sylvain
  • Rémila, Eric
  • Solal, Philippe

Abstract

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

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:26578
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    References listed on IDEAS

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    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. 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.
    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. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    7. 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.
    8. 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. 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.
    3. 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.
    4. 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.
    5. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.

    More about this item

    Keywords

    Core; excess function; dominance path; Davis-Maschler reduced-game;

    JEL classification:

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

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