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Axiomatizations of the core on the universal domain and other natural domains


Author Info

  • Peter Sudhölter

    (Institute of Mathematical Economics, University of Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany)

  • Yan-An Hwang

    (National Dong Hua University, Hualien, Taiwan)


We prove that the core on the set of all transferable utility games with players contained in a universe of at least five members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness, the weak reduced game property, the converse reduced game property, and the reconfirmation property. These properties also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games, and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on sets of nontransferable utility games.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 29 (2001)
Issue (Month): 4 ()
Pages: 597-623

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Handle: RePEc:spr:jogath:v:29:y:2001:i:4:p:597-623

Note: Received September 1999/Final version December 2000
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Keywords: TU game · core · kernel; NTU game.;


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Cited by:
  1. repec:hal:journl:halshs-00673909 is not listed on IDEAS
  2. Albizuri, M. Josune & Sudhölter, Peter, 2014. "On the Core of Games with Communication Structures," Discussion Papers of Business and Economics 6/2014, Department of Business and Economics, University of Southern Denmark.
  3. Yan-An Hwang, 2006. "Two characterizations of the consistent egalitarian solution and of the core on NTU games," Computational Statistics, Springer, vol. 64(3), pages 557-568, December.
  4. Yan-An Hwang & Yu-Hsien Liao, 2011. "The multi-core, balancedness and axiomatizations for multi-choice games," International Journal of Game Theory, Springer, vol. 40(4), pages 677-689, November.
  5. repec:hal:cesptp:halshs-00950109 is not listed on IDEAS
  6. Grabisch, Michel & Sudhölter, Peter, 2014. "On the restricted cores and the bounded core of games on distributive lattices," European Journal of Operational Research, Elsevier, vol. 235(3), pages 709-717.
  7. Orshan, Guni & Sudhölter, Peter, 2010. "Nonsymmetric variants of the prekernel and the prenucleolus," Discussion Papers of Business and Economics 1/2010, Department of Business and Economics, University of Southern Denmark.
  8. Yan-An Hwang & Yu-Hsien Liao, 2010. "The unit-level-core for multi-choice games: the replicated core for TU games," Journal of Global Optimization, Springer, vol. 47(2), pages 161-171, June.
  9. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer, vol. 41(4), pages 885-898, November.
  10. Yan-An Hwang, 2013. "On the core: complement-reduced game and max-reduced game," International Journal of Game Theory, Springer, vol. 42(2), pages 339-355, May.
  11. Michel Grabisch & Peter Sudhölter, 2012. "The Bounded Core for Games with Precedence Constraints," PSE - Labex "OSE-Ouvrir la Science Economique" hal-00759893, HAL.
  12. Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer, vol. 39(1), pages 113-136, March.
  13. Gooni Orshan & Peter Sudholter, 2001. "Reconfirming the Prenucleolus," Discussion Paper Series dp267, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  14. repec:hal:cesptp:hal-00759893 is not listed on IDEAS
  15. Llerena, Francesc, 2007. "An axiomatization of the core of games with restricted cooperation," Economics Letters, Elsevier, vol. 95(1), pages 80-84, April.


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