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An efficient Shapley value for games with fuzzy characteristic function

Author

Listed:
  • Mallozzi, Lina
  • Vidal-Puga, Juan

Abstract

We consider cooperative games where the characteristic function is valued in the space of the fuzzy numbers. By using different fuzzy calculation methods to transform the game into a crisp cooperative one, we define and characterize an efficient extension of the Shapley value. This solution is a relevant member of a wider family of more general, fuzzy calculation method dependent extensions of the Shapley value.

Suggested Citation

  • Mallozzi, Lina & Vidal-Puga, Juan, 2024. "An efficient Shapley value for games with fuzzy characteristic function," MPRA Paper 122168, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:122168
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    References listed on IDEAS

    as
    1. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    2. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. K. Michael Ortmann, 2000. "The proportional value for positive cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 235-248, April.
    4. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cooperative game; Shapley value; fuzzy set; efficiency;
    All these keywords.

    JEL classification:

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

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