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 On coset weighted potential game Wang, Yuanhua1; Cheng, Daizhan2 2020-06-01 Source Publication JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS ISSN 0016-0032 Volume 357Issue:9Pages:5523-5540 Abstract In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify whether a finite game is a coset weighted potential game, and a simple formula is obtained to calculate the corresponding potential function. Then some properties of coset weighted potential games are revealed. Finally, by resorting to the vector space structure of finite games, a new orthogonal decomposition based on coset weights is proposed, the corresponding geometric and algebraic expressions of all the subspaces are given by providing their bases. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. DOI 10.1016/j.jfranklin.2020.02.040 Indexed By SCI Language 英语 Funding Project National Natural Science Foundation of China[61903236] ; National Natural Science Foundation of China[61773371] ; National Natural Science Foundation of China[61876101] ; National Natural Science Foundation of China[71701115] WOS Research Area Automation & Control Systems ; Engineering ; Mathematics WOS Subject Automation & Control Systems ; Engineering, Multidisciplinary ; Engineering, Electrical & Electronic ; Mathematics, Interdisciplinary Applications WOS ID WOS:000577473000019 Publisher PERGAMON-ELSEVIER SCIENCE LTD Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/52350 Collection 中国科学院数学与系统科学研究院 Corresponding Author Wang, Yuanhua Affiliation 1.Shandong Normal Univ, Sch Business, Jinan 250014, Peoples R China2.Chinese Acad Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China Recommended CitationGB/T 7714 Wang, Yuanhua,Cheng, Daizhan. On coset weighted potential game[J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,2020,357(9):5523-5540. APA Wang, Yuanhua,&Cheng, Daizhan.(2020).On coset weighted potential game.JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,357(9),5523-5540. MLA Wang, Yuanhua,et al."On coset weighted potential game".JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 357.9(2020):5523-5540.
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