International Journal of Game Theory

, Volume 29, Issue 4, pp 597–623

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

Authors

  • Yan-An Hwang
    • National Dong Hua University, Hualien, Taiwan
  • Peter Sudhölter
    • Institute of Mathematical Economics, University of Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany (E-mail: psudhoelter@wiwi.uni-bielefeld.de)

DOI: 10.1007/s001820100060

Cite this article as:
Hwang, Y. & Sudhölter, P. Game Theory (2001) 29: 597. doi:10.1007/s001820100060
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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.

Key words: TU gamecorekernel; NTU game.
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© Springer-Verlag Berlin Heidelberg 2001