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On core stability, vital coalitions, and extendability

  • Shellshear, Evan
  • Sudhölter, Peter

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. 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.
  2. 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.
  3. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185.
  4. T. Raghavan & Peter Sudhölter, 2005. "The modiclus and core stability," International Journal of Game Theory, Springer, vol. 33(4), pages 467-478, November.
  5. 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.
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