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Stabilization of evolutionary networked games with length-r information

Author

Listed:
  • Mao, Ying
  • Wang, Liqing
  • Liu, Yang
  • Lu, Jianquan
  • Wang, Zhen

Abstract

This paper investigates the dynamics of evolutionary networked games with different length information via semi-tensor product (STP) method. First, a networked game with different length information is modeled in the form of probabilistic Boolean networks (PBNs) with time delays. Second, based on the utility function of each player, a necessary condition for the existence of a pure Nash equilibrium is obtained. Then a state feedback control is applied to stabilize the considered system. Finally, an example is presented to substantiate the effectiveness of the theoretical results.

Suggested Citation

  • Mao, Ying & Wang, Liqing & Liu, Yang & Lu, Jianquan & Wang, Zhen, 2018. "Stabilization of evolutionary networked games with length-r information," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 442-451.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:442-451
    DOI: 10.1016/j.amc.2018.05.027
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    References listed on IDEAS

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    1. Fangfei Li, 2016. "Feedback control design for the complete synchronisation of two coupled Boolean networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(12), pages 2996-3003, September.
    2. Anna Nagurney & Dong Li, 2015. "A supply chain network game theory model with product differentiation, outsourcing of production and distribution, and quality and price competition," Annals of Operations Research, Springer, vol. 226(1), pages 479-503, March.
    3. Tong, Liyun & Liu, Yang & Lou, Jungang & Lu, Jianquan & Alsaadi, Fuad E., 2018. "Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 263-275.
    4. Li, Meilin & Lu, Jianquan & Lou, Jungang & Liu, Yang & Alsaadi, Fuad E., 2018. "The equivalence issue of two kinds of controllers in Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 633-640.
    5. Wang, Liqing & Liu, Yang & Wu, Zhengguang & Alsaadi, Fuad E., 2018. "Strategy optimization for static games based on STP method," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 390-399.
    6. T. Başar & R. Srikant, 2002. "A Stackelberg Network Game with a Large Number of Followers," Journal of Optimization Theory and Applications, Springer, vol. 115(3), pages 479-490, December.
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    Cited by:

    1. Xinrong Yang & Zhenping Geng & Haitao Li, 2023. "Matrix-Based Method for the Analysis and Control of Networked Evolutionary Games: A Survey," Games, MDPI, vol. 14(2), pages 1-13, February.
    2. Zhong, Jie & Liu, Yang & Kou, Kit Ian & Sun, Liangjie & Cao, Jinde, 2019. "On the ensemble controllability of Boolean control networks using STP method," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 51-62.

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