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Matrix expression of Shapley values and its application to distributed resource allocation
Wang, Yuanhua1; Cheng, Daizhan2; Liu, Xiyu1
2019-02-01
Source PublicationSCIENCE CHINA-INFORMATION SCIENCES
ISSN1674-733X
Volume62Issue:2Pages:11
AbstractThe symmetric and weighted Shapley values for cooperative n-person games are studied. Using the semi-tensor product of matrices, it is first shown that a characteristic function can be expressed as a pseudo-Boolean function. Then, two simple matrix formulas are obtained for calculating the symmetric and weighted Shapley values. Finally, using these new formulas, a design technique for the agents' payoff functions in distributed resource allocation problems is proposed. It is possible to design payoff functions with the weighted Shapley value by the nonsymmetric weights defined on the players, thus ensuring that the optimal allocation is a pure Nash equilibrium. Practical examples are presented to illustrate the theoretical results.
Keywordsemi-tensor product of matrices Shapley value matrix formula distributed resource allocation
DOI10.1007/s11432-018-9414-5
Language英语
Funding ProjectNational Natural Science Foundation of China[61773371]
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000454513000001
PublisherSCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32134
Collection系统科学研究所
Affiliation1.Shandong Normal Univ, Sch Management Sci & Engn, Jinan 250014, Shandong, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Wang, Yuanhua,Cheng, Daizhan,Liu, Xiyu. Matrix expression of Shapley values and its application to distributed resource allocation[J]. SCIENCE CHINA-INFORMATION SCIENCES,2019,62(2):11.
APA Wang, Yuanhua,Cheng, Daizhan,&Liu, Xiyu.(2019).Matrix expression of Shapley values and its application to distributed resource allocation.SCIENCE CHINA-INFORMATION SCIENCES,62(2),11.
MLA Wang, Yuanhua,et al."Matrix expression of Shapley values and its application to distributed resource allocation".SCIENCE CHINA-INFORMATION SCIENCES 62.2(2019):11.
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