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Modeling and optimization for networked evolutionary games with player exit mechanism: Semi-tensor product of matrices method

Author

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  • Tang, Yu
  • Li, Lulu
  • Lu, Jianquan

Abstract

This study investigates a class of networked evolutionary games (NEGs) with player exit mechanisms through the matrices semi-tensor product (STP) method for the first time. In these NEGs, the behavior of players changing strategies at the same time is similar to cellular automata. Firstly, the player’s exit is identified as a “virtual” strategy. This strategy will be chosen by players whose payoff is below a threshold and will not be changed. Based on this identification, a new strategy updating rule is proposed. Secondly, by using the method of STP, the NEGs with player exit mechanisms are formulated as an iterative matrix equation. Furthermore, a control sequence is designed to minimize the number of exiting players by analyzing the structure of the iterative matrix. Finally, the validity of our new results is illustrated by an example of the opinion evolution.

Suggested Citation

  • Tang, Yu & Li, Lulu & Lu, Jianquan, 2022. "Modeling and optimization for networked evolutionary games with player exit mechanism: Semi-tensor product of matrices method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    • Handle: RePEc:eee:phsmap:v:590:y:2022:i:c:s0378437121009274
    DOI: 10.1016/j.physa.2021.126710
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    1. Wang, Yadong & Wang, Delu & Shi, Xunpeng, 2021. "Exploring the dilemma of overcapacity governance in China's coal industry: A tripartite evolutionary game model," Resources Policy, Elsevier, vol. 71(C).
    2. Haitao Li & Xueying Ding & Qiqi Yang & Yingrui Zhou, 2018. "Algebraic Formulation and Nash Equilibrium of Competitive Diffusion Games," Dynamic Games and Applications, Springer, vol. 8(2), pages 423-433, June.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Du, Wen-Bo & Cao, Xian-Bin & Zhao, Lin & Hu, Mao-Bin, 2009. "Evolutionary games on scale-free networks with a preferential selection mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4509-4514.
    5. Li, Fangfei & Li, Jianning & Shen, Lijuan, 2018. "State feedback controller design for the synchronization of Boolean networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1267-1276.
    6. Wang, Si-Yi & Liu, Yan-Ping & Zhang, Feng & Wang, Rui-Wu, 2021. "Super-rational aspiration induced strategy updating promotes cooperation in the asymmetric prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    7. Zhao, Guodong & Wang, Yuzhen & Li, Haitao, 2016. "A matrix approach to modeling and optimization for dynamic games with random entrance," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 9-20.
    8. Li, Yumeng & Zhang, Jun & Perc, Matjaž, 2018. "Effects of compassion on the evolution of cooperation in spatial social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 437-443.
    9. G. Papavassilopoulos, 2013. "University-Students Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 387-418, September.
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    Cited by:

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    3. Jirui Li & Junsheng Xiao & Jie Yuan, 2023. "Two-Tier Cooperation Based High-Reliable and Lightweight Forwarding Strategy in Heterogeneous WBAN," Sustainability, MDPI, vol. 15(6), pages 1-24, March.

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