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An optimal bound to access the core in TU-games

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

Abstract

For any transferable utility game in coalitional form with a 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 at most n-1, where n is the number of players. This bound exploits the geometry of the core and is optimal. It considerably improves the upper bounds found so far by Koczy (2006), Yang (2010, 2011) and a previous result by ourselves (2012) in which the bound was n(n-1)/2.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 38972.

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Date of creation: 23 May 2012
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Handle: RePEc:pra:mprapa:38972

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Keywords: Core ; Block ; Weak dominance relation ; Strong dominance relation ; Davis-Maschler reduced games;

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References

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  1. Kóczy,László Á., 2005. "The Core Can Be Accessed with a Bounded Number of Blocks," Research Memorandum 042, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  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. Kamal Jain & Rakesh Vohra, 2010. "Extendability and von Neuman–Morgenstern stability of the core," International Journal of Game Theory, Springer, vol. 39(4), pages 691-697, October.
  5. Shellshear, Evan & Sudhölter, Peter, 2009. "On core stability, vital coalitions, and extendability," Games and Economic Behavior, Elsevier, vol. 67(2), pages 633-644, November.
  6. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
  7. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
  8. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer, vol. 18(2), pages 185-87.
  9. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  10. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
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Cited by:
  1. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Computational Statistics, Springer, vol. 78(2), pages 187-202, October.

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