Consistency Properties of the Nontransferable Cooperative Game Solutions

  • Elena Yanovskaya
Part of the Theory and Decision Library book series (TDLC, volume 18)

Abstract

We consider solutions of NTU cooperative games defined with help of an excess function — the ε-core, the prenucleolus, the prekernel. It is shown that both the prenucleolus and the prekernel don’t possess the reduced game property and the converse reduced game property for all excess functions satisfying the Kalai’s (Kalai (1978)) conditions. The ε-core may possess these properties or not in dependence on excess functions. Axiomatic characterizations of the ε-core for arbitrary fixed ε and of the collection of ε-cores for all ε and for a particular excess function are given.

Keywords

Cooperative Game Payoff Vector Excess Function Axiomatic Characterization Game Property 
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References

  1. Dutta B.(1990) The Egalitarian Solution and the Reduced Game Properties in Convex Games. International Journal of Game Theory, 19, 153–169.CrossRefGoogle Scholar
  2. Kalai E.(1978) Excess Functions for Cooperative Games without Sidepaymentts. SIAM Journal of Appl. Math. 20, 1, 60–71.Google Scholar
  3. Maschler M.(1992) The bargaining set, kernel and nucleolus in: Aumann R., Hart S. eds. Handbook of Game Theory, v.1, Elsevier Sci.Publishers, pp.591–663.Google Scholar
  4. Peleg B.(1985) An axiomatization of the core of cooperative games without side payments, Journal of Math. Economics, 14, 203–214.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Elena Yanovskaya
    • 1
  1. 1.Insitute for Economics and MathematicsRussian Academy of SciencesSt. PetersburgRussia

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