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On core stability, vital coalitions, and extendability

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Author Info

  • Shellshear, Evan
  • Sudhölter, Peter

Abstract

If a TU game is extendable, then its core is a stable set. However, there are many TU games with a stable core that are not extendable. A coalition is vital if there exists some core element x such that none of the proper subcoalitions is effective for x. It is exact if it is effective for some core element. If all coalitions that are vital and exact are extendable, then the game has a stable core. It is shown that the contrary is also valid for matching games, for simple flow games, and for minimum coloring games.

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File URL: http://www.sciencedirect.com/science/article/B6WFW-4VG7MS8-1/2/e04bb4dfb90f2cc4e10dd4bc538277cf
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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 67 (2009)
Issue (Month): 2 (November)
Pages: 633-644

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Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:633-644

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: TU game Core Stable set Extendability Vital coalition;

References

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  1. T. Raghavan & Peter Sudhölter, 2005. "The modiclus and core stability," International Journal of Game Theory, Springer, vol. 33(4), pages 467-478, November.
  2. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185.
  3. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
  4. Yaron Azrieli & Ehud Lehrer, 2007. "Extendable Cooperative Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 1069-1078, December.
  5. J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer, vol. 28(2), pages 211-227.
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Cited by:
  1. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "An optimal bound to access the core in TU-games," MPRA Paper 38972, University Library of Munich, Germany.
  2. 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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