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Stochastic stability and stabilization of n-person random evolutionary Boolean games

Author

Listed:
  • Ding, Xueying
  • Li, Haitao
  • Yang, Qiqi
  • Zhou, Yingrui
  • Alsaedi, Ahmed
  • Alsaadi, Fuad E.

Abstract

This paper studies the stochastic stability and stabilization of n-person random evolutionary Boolean games (REBG). Firstly, the n-person REBG is converted to an algebraic form by using the semi-tensor product of matrices. Secondly, a necessary and sufficient condition is presented for the stochastic stability of n-person REBG based on the algebraic form. Thirdly, a constructive procedure is proposed for the state feedback stochastic stabilization control design of n-person REBG by defining a series of stochastic reachable sets. Finally, two illustrative examples are worked out to show the effectiveness of the obtained new results.

Suggested Citation

  • Ding, Xueying & Li, Haitao & Yang, Qiqi & Zhou, Yingrui & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "Stochastic stability and stabilization of n-person random evolutionary Boolean games," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 1-12.
    • Handle: RePEc:eee:apmaco:v:306:y:2017:i:c:p:1-12
    DOI: 10.1016/j.amc.2017.02.020
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    References listed on IDEAS

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    1. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
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    Cited by:

    1. Li, Yalu & Li, Haitao & Li, Yuanyuan, 2021. "Constrained set controllability of logical control networks with state constraints and its applications," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    2. Li, Xiaopeng & Sun, Shiwen & Xia, Chengyi, 2019. "Reputation-based adaptive adjustment of link weight among individuals promotes the cooperation in spatial social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 810-820.
    3. Li, Haitao & Xu, Xiaojing & Ding, Xueying, 2019. "Finite-time stability analysis of stochastic switched boolean networks with impulsive effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 557-565.
    4. Guo, Peilian & Han, Changda, 2021. "Nash equilibrium and group strategy consensus of networked evolutionary game with coupled social groups," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    5. 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.

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