International Journal of Game Theory

, Volume 6, Issue 4, pp 249–255 | Cite as

A generalization of theKohlberg criterion

Papers

Abstract

TheKohlberg criterion, which characterizes the nucleolus of a game (over the set of all imputations) in terms of balanced collections, is here extended to the sets of payoff vectors for various coalition structures. It is shown that one generalization yields a necessary condition; another yields a sufficient condition. A necessary and sufficient condition — which is unfortunately somewhat difficult to verify — is also given.

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References

  1. Farkas, J.: Über die Theorie der Einfachen Ungleichungen, J. Reine Angew. Math.124, 1901, 1–27.Google Scholar
  2. Kohlberg, E.: On the Nucleolus of a Characteristic Function Game. SIAM J. Appl. Math20, 1971, 62–66.Google Scholar
  3. Schmeidler, D.: The Nucleolus of a Characteristic Function Game. SIAM J. Appl. Math.17, 1969, 1163–1170.Google Scholar
  4. Shapley, L.S.: On Balanced Sets and Cores. Naval Res. Log. Quart.14, 1967, 453–460.Google Scholar

Copyright information

© Physica-Verlag 1977

Authors and Affiliations

  • G. Owen
    • 1
  1. 1.Department of Mathematical SciencesRice UniversityHouston

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