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Fuzzy Cores and Fuzzy Balancedness

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  • van Gulick, G.

    (Tilburg University, Center For Economic Research)

  • Norde, H.W.

    (Tilburg University, Center For Economic Research)

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
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • van Gulick, G. & Norde, H.W., 2011. "Fuzzy Cores and Fuzzy Balancedness," Discussion Paper 2011-062, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:5792b50b-8b99-46dd-bba5-435b1d607152
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    References listed on IDEAS

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    1. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper 2002-13, Tilburg University, Center for Economic Research.
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    3. van Gulick, Gerwald & Borm, Peter & De Waegenaere, Anja & Hendrickx, Ruud, 2010. "Deposit games with reinvestment," European Journal of Operational Research, Elsevier, vol. 200(3), pages 788-799, February.
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    6. Branzei, R. & Tijs, S.H., 2003. "On convex fuzzy games," Other publications TiSEM b53ebd70-807d-46cf-a854-f, Tilburg University, School of Economics and Management.
    7. Tijs, S.H. & Brânzei, R. & Ishihara, S. & Muto, S., 2004. "On cores and stable sets for fuzzy games," Other publications TiSEM 66dd20be-cb4b-4b6d-937e-0, Tilburg University, School of Economics and Management.
    8. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
    9. Jean-Pierre Aubin, 1981. "Cooperative Fuzzy Games," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 1-13, February.
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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;
    All these keywords.

    JEL classification:

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

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