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.
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Acknowledgement
This work was supported in part by the National Natural Science Foundation of China under grant No. 72071032, the Social Science Planning Program of Fujian Province of China under Grant FJ2018B014, and the Special Foundation Program for Science and Technology Innovation of Fujian Agriculture and Forestry University of China under Grant CXZX2020043S.
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Liu, JC., Li, DF. Improved Shapley Values Based on Players’ Least Square Contributions and Their Applications in the Collaborative Profit Sharing of the Rural E-commerce. Group Decis Negot 31, 7–22 (2022). https://doi.org/10.1007/s10726-021-09741-2
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DOI: https://doi.org/10.1007/s10726-021-09741-2