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The Extension of Combinatorial Solutions for Cooperative Games

  • Jiang-Xia Nan
  • Li-Xiao Wei
  • Mao-Jun ZhangEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1082)

Abstract

In this paper, a new model to solve the social selfish coefficient \( \alpha \in \left[ {0,1} \right] \) for the \( \alpha \)-egalitarian Shapley values and a new convex combinations of single-value in terms of a coalition forming weight coefficient \( \beta \in \left[ {0,1} \right] \), which is called the SCE value for cooperative games are presented. The efficiency, linearity, symmetry and \( \alpha \)-dummy player property of the SCE value are proved. By proposing a procedural interpretation, we define the \( \beta \) as the coalition forming weight (or possibility) coefficient and find a new way of assigning the grand coalition profit among all players is coincided with the SCE value which verify the SCE value’s validity, applicability and superiority.

Keywords

Cooperative games Egalitarian Shapley value \( \alpha \)-CIS value SCE value 

Notes

Acknowledgement

The authors would like to thank the associate editor and also appreciate the constructive suggestions from the anonymous referees. This research was supported by the key Program of National Natural Science Foundation of China (No. 71231003), the Natural Science Foundation of China (Nos. 71461005 and 71561008). The Innovation Project of Guet Graduate Education (No. 2019YCXS082).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilinChina

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