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A Union Self-evaluation Approach to Associated Consistency for Cooperative Games

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Abstract

Xu et al. (Linear Algebra Appl 430(11):2896–2897, 2009) introduced the notion of associated consistency according to the idea of “individual self-evaluation". In this paper, we introduce a new type of associated consistency according to the idea of “union self-evaluation" instead of “individual self-evaluation". Adopting this type of associated consistency, we provide new axiomatizations of the equal allocation of non-separable contributions (EANSC) value and the center-of-gravity of the imputation set (CIS) value. Moreover, a dynamic process is given based on the type of associated games, which leads to the CIS value and EANSC value, starting from an arbitrary efficient payoff vector.

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Notes

  1. The detailed proofs of these results can be obtained from the authors on request.

  2. A solution \(\varphi \) satisfies linearity if \(\varphi (N,av+bw)=a\varphi (N,v)+b\varphi (N,w)\) for all \(\langle N,v \rangle , \langle N,w \rangle \in {\mathscr {G}}^N\) and \(a, b \in \mathbb {R}\)

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Acknowledgements

The authors thank an editor and two anonymous referees for very helpful comments and suggestions. This work is supported by the National Natural Science Foundation of China (Grant Nos. 72301214 and 72071159), National Key R &D Program of China (Grant No. 2021YFA1000402) and Fundamental Research Funds for the Central Universities (Grant Nos. D5000230178).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, China

    Wenzhong Li & Genjiu Xu

  2. International Joint Research Center on Operations Research, Optimization and Artificial Intelligence, Xi’an, 710072, Shaanxi, China

    Wenzhong Li, Genjiu Xu & René van den Brink

  3. MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University, Xi’an, 710129, Shaanxi, China

    Wenzhong Li

  4. Department of Economics, VU University, De Boelelaan 1105, 1081 HV, Amsterdam, The Netherlands

    René van den Brink

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  1. Wenzhong Li
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  2. Genjiu Xu
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  3. René van den Brink
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Correspondence to Genjiu Xu.

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Communicated by Kyriakos G. Vamvoudakis.

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Li, W., Xu, G. & van den Brink, R. A Union Self-evaluation Approach to Associated Consistency for Cooperative Games. J Optim Theory Appl 199, 863–880 (2023). https://doi.org/10.1007/s10957-023-02322-0

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  • DOI: https://doi.org/10.1007/s10957-023-02322-0

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