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Improved Shapley Values Based on Players’ Least Square Contributions and Their Applications in the Collaborative Profit Sharing of the Rural E-commerce

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  • Jia-Cai Liu

    (Fujian Agriculture and Forestry University)

  • Deng-Feng Li

    (University of Electronic Science and Technology of China)

Abstract

In this paper, we introduce several improved Shapley values for cooperative transferable utility (TU) games depending on the players’ least square contributions instead of their marginal contributions. This work is mainly enlightened by the Shapley value and the player’s productivity-based excess (usually called the excess of the player). Based on the player’s contribution-based excess, two quadratic programming models for obtaining the players’ (weighted) least square contributions are constructed. The efficient weighted Shapley-like value proposed in this paper as an extension of the Shapley value can be characterized by four independent axioms such as the symmetry, the efficiency, the additivity, and the quasi-null player, which are almost similar to the Shapley value’s four axioms except that the anonymity is replaced with the quasi-null player. The four axioms are proven to uniquely determine the efficient weighted Shapley-like value. Finally, the advantages of the proposed values are illustrated with a real case about the collaborative profit sharing of the rural e-commerce.

Suggested Citation

  • Jia-Cai Liu & Deng-Feng Li, 2022. "Improved Shapley Values Based on Players’ Least Square Contributions and Their Applications in the Collaborative Profit Sharing of the Rural E-commerce," Group Decision and Negotiation, Springer, vol. 31(1), pages 7-22, February.
    • Handle: RePEc:spr:grdene:v:31:y:2022:i:1:d:10.1007_s10726-021-09741-2
    DOI: 10.1007/s10726-021-09741-2
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