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Choquet Extension Of Cooperative Games

Author

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  • CHUNQIAO TAN

    (School of Business, Central South University, Changsha 410083, P. R. China)

  • ZHONG-ZHONG JIANG

    (School of Business, Central South University, Changsha 410083, P. R. China)

  • XIAOHONG CHEN

    (School of Business, Central South University, Changsha 410083, P. R. China)

Abstract

A multilinear extension of the n-person cooperative game was introduced by Owen in 1972, and a new extension method is proposed in this paper. For n-person cooperative games, any coalition can equivalently be represented by its characteristic vectors. By means of the Choquet integral, a new fuzzy extension, called the Choquet extension, is developed. Furthermore, a Shapley function in this class of fuzzy cooperative games with the Choquet extension form is defined. Axioms of the Shapley function are proposed, and an explicit formula for the Shapley function is given. Finally, an equivalent definition of this Shapley function is discussed.

Suggested Citation

  • Chunqiao Tan & Zhong-Zhong Jiang & Xiaohong Chen, 2013. "Choquet Extension Of Cooperative Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-20.
    • Handle: RePEc:wsi:apjorx:v:30:y:2013:i:04:n:s021759591350005x
    DOI: 10.1142/S021759591350005X
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    References listed on IDEAS

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    1. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, January.
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    Cited by:

    1. Chunqiao Tan & Wenrui Feng & Weibin Han, 2020. "On the Banzhaf-like Value for Cooperative Games with Interval Payoffs," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    2. Fanyong Meng & Xiaohong Chen, 2016. "Cooperative Fuzzy Games with Convex Combination Form," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-25, February.

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