{"title":"Stability of networked evolutionary games with payoff perturbation","authors":"Ziyun Wang, Xiaoyu Zhao, Shihua Fu","doi":"10.1049/cth2.12741","DOIUrl":null,"url":null,"abstract":"<p>In networked evolutionary games (NEGs), some elements in the payoff matrix of players may change due to environmental factors. In this article, the stability of NEGs with payoff perturbation is studied using the semi-tensor product (STP) of matrices, and some new results are given. First, the perturbation of a column of the payoff matrix is considered, and a necessary and sufficient condition to ensure that the transition matrix of the profiles evolution dynamics to remain unchanged is provided. Second, the case that multiple columns of the game profile transition matrix are perturbed is investigated, and a necessary and sufficient condition for the stability of the NEGs is proposed. Finally, the validity of the results is illustrated by an example.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"18 17","pages":"2390-2397"},"PeriodicalIF":2.2000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12741","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IET Control Theory and Applications","FirstCategoryId":"94","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1049/cth2.12741","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
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Abstract
In networked evolutionary games (NEGs), some elements in the payoff matrix of players may change due to environmental factors. In this article, the stability of NEGs with payoff perturbation is studied using the semi-tensor product (STP) of matrices, and some new results are given. First, the perturbation of a column of the payoff matrix is considered, and a necessary and sufficient condition to ensure that the transition matrix of the profiles evolution dynamics to remain unchanged is provided. Second, the case that multiple columns of the game profile transition matrix are perturbed is investigated, and a necessary and sufficient condition for the stability of the NEGs is proposed. Finally, the validity of the results is illustrated by an example.
期刊介绍：
IET Control Theory & Applications is devoted to control systems in the broadest sense, covering new theoretical results and the applications of new and established control methods. Among the topics of interest are system modelling, identification and simulation, the analysis and design of control systems (including computer-aided design), and practical implementation. The scope encompasses technological, economic, physiological (biomedical) and other systems, including man-machine interfaces.
Most of the papers published deal with original work from industrial and government laboratories and universities, but subject reviews and tutorial expositions of current methods are welcomed. Correspondence discussing published papers is also welcomed.
Applications papers need not necessarily involve new theory. Papers which describe new realisations of established methods, or control techniques applied in a novel situation, or practical studies which compare various designs, would be of interest. Of particular value are theoretical papers which discuss the applicability of new work or applications which engender new theoretical applications.
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