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Vector Space Structure of Finite Evolutionary Games and Its Application to Strategy Profile Convergence
Qi Hongsheng1; Wang Yuanhua2; Liu Ting1; Cheng Daizhan1,2
2016-06-01
Source PublicationJOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN1009-6124
Volume29Issue:3Pages:602-628
AbstractA 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.
KeywordEvolutionary game Lyapunov function Nash equilibrium near potential function potential
DOI10.1007/s11424-016-4192-7
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000379826000003
PublisherSPRINGER HEIDELBERG
Citation statistics
Cited Times:7[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23229
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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