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

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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)

Abstract

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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Related research

Keywords: TU game · core · kernel; NTU game.;

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Cited by:
  1. Grabisch, Michel & Sudhölter, Peter, 2012. "On the restricted cores and the bounded core of games on distributive lattices," Discussion Papers of Business and Economics 22/2012, Department of Business and Economics, University of Southern Denmark.
  2. Michel Grabisch & Peter Sudhölter, 2012. "The bounded core for games with precedence constraints," Documents de travail du Centre d'Economie de la Sorbonne 12006, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Orshan,G. & Sudhoelter,P., 2001. "The positive core of a cooperative game," Working Papers 326, Bielefeld University, Center for Mathematical Economics.
  4. repec:hal:journl:halshs-00673909 is not listed on IDEAS
  5. 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.
  6. 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.
  7. Llerena, Francesc, 2007. "An axiomatization of the core of games with restricted cooperation," Economics Letters, Elsevier, vol. 95(1), pages 80-84, April.
  8. 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.
  9. 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.
  10. 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.
  11. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer, vol. 41(4), pages 885-898, November.
  12. Gooni Orshan & Peter Sudholter, 2001. "Reconfirming the Prenucleolus," Discussion Paper Series dp267, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  13. repec:hal:cesptp:hal-00759893 is not listed on IDEAS
  14. Guni Orshan & Peter Sudhölter, 2012. "Nonsymmetric variants of the prekernel and the prenucleolus," International Journal of Game Theory, Springer, vol. 41(4), pages 809-828, November.
  15. repec:hal:cesptp:halshs-00950109 is not listed on IDEAS
  16. repec:hal:cesptp:halshs-00673909 is not listed on IDEAS

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