Matrix expression of Shapley values and its application to distributed resource allocation

doi:10.1007/s11432-018-9414-5

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	Matrix expression of Shapley values and its application to distributed resource allocation
	Wang, Yuanhua 1; Cheng, Daizhan2 ; Liu, Xiyu 1
	2019-02-01
发表期刊	SCIENCE CHINA-INFORMATION SCIENCES
ISSN	1674-733X
卷号	62 期号:2 页码:11
摘要	The 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.
关键词	semi-tensor product of matrices Shapley value matrix formula distributed resource allocation
DOI	10.1007/s11432-018-9414-5
语种	英语
资助项目	National Natural Science Foundation of China[61773371]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000454513000001
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32134
专题	系统科学研究所
通讯作者	Wang, Yuanhua
作者单位	1.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
推荐引用方式 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.