KMS Of Academy of mathematics and systems sciences, CAS
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 | |
发表期刊 | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY |
ISSN | 1009-6124 |
卷号 | 29期号:3页码:602-628 |
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. |
关键词 | Evolutionary game Lyapunov function Nash equilibrium near potential function potential |
DOI | 10.1007/s11424-016-4192-7 |
语种 | 英语 |
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 |
WOS类目 | Mathematics, Interdisciplinary Applications |
WOS记录号 | WOS:000379826000003 |
出版者 | SPRINGER HEIDELBERG |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/23229 |
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. |
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