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The Shapley value for fuzzy games: TU games approach

Author

Listed:
  • Yu-Hsien Liao

    (Department of Applied Mathematics, National Pingtung University of Education, Taiwan)

Abstract

In this note we investigate the Shapley value for fuzzy games proposed by Hwang and Liao (2009). We show that there exists a transferable-utility (TU) decomposition games that can be adopted to characterize the fuzzy Shapley value, i.e., the fuzzy Shapley value consists of the Shapley value of the corresponding TU decomposition games.

Suggested Citation

  • Yu-Hsien Liao, 2013. "The Shapley value for fuzzy games: TU games approach," Economics Bulletin, AccessEcon, vol. 33(1), pages 192-197.
    • Handle: RePEc:ebl:ecbull:eb-12-00576
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    4. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    5. Jean-Pierre Aubin, 1981. "Cooperative Fuzzy Games," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 1-13, February.
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    More about this item

    Keywords

    Fuzzy games; TU decomposition games.;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C0 - Mathematical and Quantitative Methods - - General

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