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Fuzzy cores and fuzzy balancedness

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  • Gerwald Gulick
  • Henk Norde

Abstract

We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (Problemy Kibernet 10:119–139, 1963 ) and Shapley (Naval Res Logist Q 14: 453–460, 1967 ). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that any fuzzy game has a non-empty core if and only if it is balanced. We also consider deposit games to illustrate the use of the main result. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Gerwald Gulick & Henk Norde, 2013. "Fuzzy cores and fuzzy balancedness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 131-146, April.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:2:p:131-146
    DOI: 10.1007/s00186-012-0417-2
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    Cited by:

    1. Liu, Jiuqiang & Tian, Hai-Yan, 2014. "Existence of fuzzy cores and generalizations of the K–K–M–S theorem," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 148-152.

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    More about this item

    Keywords

    Cooperative fuzzy games; Fuzzy balancedness; Fuzzy core; C71;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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