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Model and Control for a Class of Networked Evolutionary Games with Finite Memories and Time-Varying Networks

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Abstract

This paper investigates the algebraic formulation and control for a class of networked evolutionary games with finite memories and time-varying networks by using the semi-tensor product method and presents a number of new results. Firstly, a kind of algebraic expressions is formulated for the given networked evolutionary games, and the dynamics of the given game is expressed as a finite homogenous Markov chain, based on which, the behaviors of the players in the corresponding evolutionary games are analyzed. Then, the control problem of the given games is studied. Under certain assumptions, the relationship between the strict Nash equilibriums and the fixed points of the given networked evolutionary games is revealed, and a free-type control sequence is designed to guarantee the Nash equilibrium reachable globally. Finally, an illustrative example is studied to support our new results.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61374065 and 61503225, the Natural Science Fund for Distinguished Young Scholars of Shandong Province under Grant JQ201613 and the Natural Science Foundation of Shandong Province under Grant ZR2015FQ003.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, People’s Republic of China

    Shihua Fu

  2. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Guodong Zhao & Haitao Li

  3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi

  4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Fuad E. Alsaadi

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  1. Shihua Fu
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  2. Guodong Zhao
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  3. Haitao Li
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  4. Ahmed Alsaedi
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  5. Fuad E. Alsaadi
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Corresponding author

Correspondence to Guodong Zhao.

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Fu, S., Zhao, G., Li, H. et al. Model and Control for a Class of Networked Evolutionary Games with Finite Memories and Time-Varying Networks. Circuits Syst Signal Process 37, 3093–3114 (2018). https://doi.org/10.1007/s00034-017-0707-2

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  • DOI: https://doi.org/10.1007/s00034-017-0707-2

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