A Matrix Approach to the Modeling and Analysis of Networked Evolutionary Games With Time Delays

Guodong Zhao; Yuzhen Wang; Haitao Li

doi:10.1109/JAS.2016.7510259

Volume 5 Issue 4

Jul. 2018

IEEE/CAA Journal of Automatica Sinica

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Guodong Zhao, Yuzhen Wang and Haitao Li, "A Matrix Approach to the Modeling and Analysis of Networked Evolutionary Games With Time Delays," IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 818-826, July 2018. doi: 10.1109/JAS.2016.7510259

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Guodong Zhao, Yuzhen Wang and Haitao Li, "A Matrix Approach to the Modeling and Analysis of Networked Evolutionary Games With Time Delays," IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 818-826, July 2018. doi: 10.1109/JAS.2016.7510259

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A Matrix Approach to the Modeling and Analysis of Networked Evolutionary Games With Time Delays

doi: 10.1109/JAS.2016.7510259

Guodong Zhao^{1
,
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Yuzhen Wang^2
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Haitao Li^1
,

1.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
2.
School of Control Science and Engineering, Shandong University, Jinan 250061, China

Funds:

the National Natural Science Foundation of China 61503225

the Natural Science Foundation of Shandong Province ZR2015FQ003

the Natural Science Foundation of Shandong Province ZR201709260273

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Author Bio:
Guodong Zhao received the B.S. degree from the School of Mathematical Science, Liaocheng University in 2010, the M.S. degree from the School of Qufu Normal University in 2013, and the Ph.D. degree from the School of Control Science and Engineering, Shandong University in 2017. His research interests include semi-tensor product of matrices, its application in networked evolutionary games theory, and logical networks theory.(e-mail: zgd_qufu@126.com)

Yuzhen Wang graduated from Tai'an Teachers College in 1986, received the M. S. degree from Shandong University of Science and Technology in 1995 and the Ph. D. degree from the Institute of Systems Science, Chinese Academy of Sciences in 2001. Since 2003, he was a professor with the School of Control Science and Engineering, Shandong University, China, and the Dean of the School of Control Science and Engineering, Shandong University. From 2001 to 2003, he worked as a Postdoctoral Fellow in Tsinghua University, Beijing, China. From Mar. 2004 to Jun. 2004, from Feb. 2006 to May 2006 and from Nov. 2008 to Jan. 2009, he visited City University of Hong Kong as a Research Fellow. From Sept. 2004 to May 2005, he worked as a visiting Research Fellow at the National University of Singapore. His research interests included nonlinear control systems, Hamiltonian systems and Boolean networks. Prof. Wang received the Prize of Guan Zhaozhi in 2002, the Prize of Huawei from the Chinese Academy of Sciences in 2001, the Prize of Natural Science from Chinese Education Ministry in 2005, and the National Prize of Natural Science of China in 2008. (e-mail: yzwang@sdu.edu.cn)

Haitao Li received the B. S. and the M. S. degrees from the School of Mathematical Science, Shandong Normal University in 2007 and 2010, respectively, and the Ph. D. degree from the School of Control Science and Engineering, Shandong University in 2014. Since 2015, he has been with the School of Mathematical Science, Shandong Normal University, China, where he is currently an associate professor. From Jan. 2014 to Jan. 2015, he worked as a Research Fellow in Nanyang Technological University, Singapore. His research interests include logical dynamic systems, switched systems, etc. He received the Prize of Best Student Paper Award at the 10th World Congress on Intelligent Control and Automation, and the Prize of Guan Zhaozhi at the 31st Chinese Control Conference. (e-mail:haitaoli09@gmail.com)
Corresponding author: Guodong Zhao, e-mail: zgd_qufu@126.com
Received Date: 2015-06-12
Accepted Date: 2015-10-13

Abstract

Abstract

Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games (NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic expression is formulated for the networked evolutionary games with finite memories, based on which the behavior of the corresponding evolutionary game is analyzed. Secondly, under a proper assumption, the existence of Nash equilibrium of the given networked evolutionary games is proved and a free-type strategy sequence is designed for the convergence to the Nash equilibrium. Finally, an illustrative example is worked out to support the obtained new results.
- Fictitious play process,
- Nash equilibrium,
- networked evolutionary games (NEGs),
- semi-tensor product of matrices

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References

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A Matrix Approach to the Modeling and Analysis of Networked Evolutionary Games With Time Delays

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