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On the number of blocks required to access the core

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

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.

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File URL: https://mpra.ub.uni-muenchen.de/26578/1/MPRA_paper_26578.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26578.

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Date of creation: 09 Nov 2010
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Handle: RePEc:pra:mprapa:26578
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  1. Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2008. "Farsighted coalitional stability in TU-games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 303-313, November.
  2. 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.
  3. 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.
  4. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
  5. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
  6. Manea, Mihai, 2007. "Core tatonnement," Journal of Economic Theory, Elsevier, vol. 133(1), pages 331-349, March.
  7. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
  8. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Game Theory Society, vol. 15(3), pages 187-200.
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