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Vector Space Structure of Finite Evolutionary Games and Its Application to Strategy Profile Convergence

文献类型：期刊论文

作者Qi Hongsheng1; Wang Yuanhua2; Liu Ting1; Cheng Daizhan1,2
刊名JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
出版日期2016-06-01
卷号29期号:3页码:602-628
关键词Evolutionary game Lyapunov function Nash equilibrium near potential function potential
ISSN号1009-6124
DOI10.1007/s11424-016-4192-7
英文摘要A vector space structure is proposed for the set of finite games with fixed numbers of players and strategies for each players. Two statical equivalences are used to reduce the dimension of finite games. Under the vector space structure the subspaces of exact and weighted potential games are investigated. Formulas are provided to calculate them. Then the finite evolutionary games (EGs) are considered. Strategy profile dynamics is obtained using different strategy updating rules (SURs). Certain SURs, which assure the convergence of trajectories to pure Nash equilibriums, are investigated. Using the vector space structure, the projection of finite games to the subspace of exact (or weighted) potential games is considered, and a simple formula is given to calculate the projection. The convergence of near potential games to an e-equilibrium is studied. Further more, the Lyapunov function of EGs is defined and its application to the convergence of EGs is presented. Finally, the near potential function for an EG is defined, and it is proved that if the near potential function of an EG is a Lyapunov function, the EG will converge to a pure Nash equilibrium. Some examples are presented to illustrate the results.
资助项目National Natural Science Foundation of China[61273013] ; National Natural Science Foundation of China[61333001] ; National Natural Science Foundation of China[61104065] ; National Natural Science Foundation of China[61374168]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000379826000003
出版者SPRINGER HEIDELBERG
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/23228]  
专题系统科学研究所
通讯作者Qi Hongsheng
作者单位1.Chinese Acad Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
2.Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China
推荐引用方式
GB/T 7714		 Qi Hongsheng,Wang Yuanhua,Liu Ting,et al. Vector Space Structure of Finite Evolutionary Games and Its Application to Strategy Profile Convergence[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2016,29(3):602-628.
APA Qi Hongsheng,Wang Yuanhua,Liu Ting,&Cheng Daizhan.(2016).Vector Space Structure of Finite Evolutionary Games and Its Application to Strategy Profile Convergence.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,29(3),602-628.
MLA Qi Hongsheng,et al."Vector Space Structure of Finite Evolutionary Games and Its Application to Strategy Profile Convergence".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 29.3(2016):602-628.

入库方式： OAI收割

来源：数学与系统科学研究院

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