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A matrix approach to modeling and optimization for dynamic games with random entrance

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  • Zhao, Guodong
  • Wang, Yuzhen
  • Li, Haitao

Abstract

This paper investigates the algebraic formulation and optimization control for a class of dynamic games with random entrance by using the semi-tensor product method, and presents a number of new results. First, the given dynamic game is considered as a kind of networked evolutionary games with switch networks, based on which, it is formulated as a Markov processes to analyze. Second, using receding horizon control method, the given game’s optimization problem is solved by a state feedback controller, when the major player is considered as a control. Finally, an illustrative example is studied to support our new results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:9-20
    DOI: 10.1016/j.amc.2016.05.012
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    References listed on IDEAS

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    1. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    2. G. Papavassilopoulos, 2013. "University-Students Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 387-418, September.
    3. Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December.
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    Cited by:

    1. Zhou, Mengyu & Liu, Xingwen & Liu, Yaojun & Hu, Qi & Shu, Feng, 2025. "Analysis and optimization control of demand response via networked evolutionary game with memory," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    2. 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.
    3. Wang, Yuanhua & Wang, Ying & Li, Haitao & Zang, Wenke, 2025. "Matrix expressions of symmetric n-player games," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    4. 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.
    5. Fu, Shihua & Cheng, Daizhan & Feng, Jun-e & Zhao, Jianli, 2021. "Matrix expression of finite Boolean-type algebras," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    6. 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).

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