Control design to minimize the number of bankrupt players for networked evolutionary games with bankruptcy mechanism

Liyuan Xia; Jianjun Wang; Shihua Fu; Yuxin Gao; Liyuan Xia; Jianjun Wang; Shihua Fu; Yuxin Gao

doi:10.3934/math.20241694

AIMS Mathematics

2024, Volume 9, Issue 12: 35702-35720. doi: 10.3934/math.20241694

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Research article

Control design to minimize the number of bankrupt players for networked evolutionary games with bankruptcy mechanism

School of Mathematical Sciences, Liaocheng University, Liaocheng 252000, China

Received: 27 September 2024 Revised: 14 November 2024 Accepted: 26 November 2024 Published: 23 December 2024
MSC : 93B52

This paper analyzed the strategy optimization problem of networked evolutionary games (NEGs) with bankruptcy mechanism. The main objective was to design a state-feedback control such that the number of bankrupt players is minimized. First, an algebraic expression was formulated for this type of NEGs by the semi-tensor product of matrices, based on which the sets of profiles with different numbers of bankrupt players are defined. Second, a desired profile set in which the number of bankrupt players is no higher than a given value was obtained, and the convergence region of this set was calculated. Third, for any profile in the convergence region of the desired set, we propose a controller design method to minimize the number of bankrupt players. Finally, an example is given to illustrate the validity of our results.
- networked evolutionary games,
- bankruptcy mechanism,
- semi-tensor product of matrices,
- minimize the number of bankrupt players
Citation: Liyuan Xia, Jianjun Wang, Shihua Fu, Yuxin Gao. Control design to minimize the number of bankrupt players for networked evolutionary games with bankruptcy mechanism[J]. AIMS Mathematics, 2024, 9(12): 35702-35720. doi: 10.3934/math.20241694

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Abstract

This paper analyzed the strategy optimization problem of networked evolutionary games (NEGs) with bankruptcy mechanism. The main objective was to design a state-feedback control such that the number of bankrupt players is minimized. First, an algebraic expression was formulated for this type of NEGs by the semi-tensor product of matrices, based on which the sets of profiles with different numbers of bankrupt players are defined. Second, a desired profile set in which the number of bankrupt players is no higher than a given value was obtained, and the convergence region of this set was calculated. Third, for any profile in the convergence region of the desired set, we propose a controller design method to minimize the number of bankrupt players. Finally, an example is given to illustrate the validity of our results.

References

[1]	Y. Hossein, S. M. Ebrahim, N. Hamidreza, S. Arash, C. Moharram, Bankruptcy-evolutionary games based solution for the multi-agent credit assignment problem, Swarm Evol. Comput., 77 (2023), 101229. https://doi.org/10.1016/J.SWEVO.2023.101229 doi: 10.1016/J.SWEVO.2023.101229
[2]	A. Furkan, S. Zubair, A. Luluwah, Applications of evolutionary game theory in urban road transport network: A state of the art review, Sustainable Cities Soc., 2023, 104791. https://doi.org/10.1016/J.SCS.2023.104791
[3]	X. Lin, Q. Jiao, L. Wang, Competitive diffusion in signed social networks: A game-theoretic perspective, Automatica, 112 (2020), 108656–108656. https://doi.org/10.1016/j.automatica.2019.108656 doi: 10.1016/j.automatica.2019.108656
[4]	T. Hamidou, A. Eitan, E. Rachid, H. Yezekael, Evolutionary games in wireless networks, IEEE Trans. Syst. Man. Cy. B., 40 (2009), 634–646. https://doi.org/10.1109/TSMCB.2009.2034631 doi: 10.1109/TSMCB.2009.2034631
[5]	W. Han, Z. Zhang, J. Sun, C. Xia, Emergence of cooperation with reputation-updating timescale in spatial public goods game, Phys. Lett. A, 393 (2021), 127173. https://doi.org/10.1016/J.PHYSLETA.2021.127173 doi: 10.1016/J.PHYSLETA.2021.127173
[6]	D. Cheng, H. Qi, Y. Zhao, An introduction to semi-tensor product of matrices and its applications, World Scientific, 2012. https://doi.org/10.1142/8323
[7]	Y. Yan, D. Cheng, J. Feng, H. Li, J. Yue, Survey on applications of algebraic state space theory of logical systems to finite state machines, Sci. China Inf. Sci., 66 (2022), 111201. https://doi.org/10.1007/S11432-022-3538-4 doi: 10.1007/S11432-022-3538-4
[8]	H. Li, X. Pang, A polynomial-time criterion for stability of large-scale switched conjunctive Boolean networks, Automatica, 159 (2024), 111340. https://doi.org/10.1016/J.AUTOMATICA.2023.111340 doi: 10.1016/J.AUTOMATICA.2023.111340
[9]	Y. Guo, P. Gong, Y. Wu, X. Sun, W. Gui, Stabilization of discrete-time switched systems with constraints by dynamic logic-based switching feedback, Automatica, 156 (2023), 111190. https://doi.org/10.1016/J.AUTOMATICA.2023.111190 doi: 10.1016/J.AUTOMATICA.2023.111190
[10]	H. Li, X. Pang, Stability analysis of large-scale Boolean networks via compositional method, Automatica, 159 (2024), 111397. https://doi.org/10.1016/J.AUTOMATICA.2023.111397 doi: 10.1016/J.AUTOMATICA.2023.111397
[11]	Y. Liu, J. Zhong, D. Ho, W. Gui, Minimal observability of Boolean networks, Sci. China Inf. Sci., 66 (2022), 152203. https://doi.org/10.1007/S11432-021-3365-2 doi: 10.1007/S11432-021-3365-2
[12]	S. Zhu, J. Lu, D Ho, J. Cao, Minimal control nodes for strong structural observability of discrete-time iteration systems: Explicit formulas and polynomial-time algorithms, IEEE Trans. Automat. Contr., 2023. https://doi.org/10.1109/tac.2023.3330263
[13]	Q. Zhu, Z. Gao, Y. Liu, W. Gui, Categorization problem on controllability of Boolean control networks, IEEE Trans. Automat. Contr., 66 (2020), 2297–2303. https://doi.org/10.1109/tac.2020.3002509 doi: 10.1109/tac.2020.3002509
[14]	Y. Wu, Y.Guo, M. Toyoda, Policy iteration approach to the infinite horizon average optimal control of probabilistic Boolean networks, IEEE Trans. Neural Networks Learn. Syst., 32 (2020), 2910–2924. https://doi.org/10.1109/TNNLS.2020.3008960 doi: 10.1109/TNNLS.2020.3008960
[15]	H. Li, X.Yang, Robust optimal control of logical control networks with function perturbation, Automatica, 152 (2023), 110970. https://doi.org/10.1016/J.AUTOMATICA.2023.110970 doi: 10.1016/J.AUTOMATICA.2023.110970
[16]	G. Zhao, Y. Wang, H. Li, A matrix approach to the modeling and analysis of networked evolutionary games with time delays, IEEE-CAA J. AUTOMATIC, 5 (2018), 818–826. https://doi.org/10.1109/jas.2016.7510259 doi: 10.1109/jas.2016.7510259
[17]	Z. Deng, T. Chen, Distributed Nash equilibrium seeking for constrained multicluster games of second-order nonlinear multiagent systems, IEEE Trans. Automat. Contr., 69 (2024), 7855–7862. https://doi.org/10.1109/tac.2024.3398064 doi: 10.1109/tac.2024.3398064
[18]	D.Cheng, F. He, H. Qi, T. Xu, Modeling, Analysis and control of networked evolutionary games, IEEE Trans. Automat. Contr., 60 (2015), 2402–2415. https://doi.org/10.1109/tac.2015.2404471 doi: 10.1109/tac.2015.2404471
[19]	P. Guo, Y. Wang, H. Li, Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method, Automatica, 49 (2013), 3384–3389. https://doi.org/10.1016/j.automatica.2013.08.008 doi: 10.1016/j.automatica.2013.08.008
[20]	Y. Zheng, C. Li, J. Feng, Modeling and dynamics of networked evolutionary game with switched time delay, IEEE Trans. Automat. Contr., 8 (2021), 1778–1787. https://doi.org/10.1109/tcns.2021.3084548 doi: 10.1109/tcns.2021.3084548
[21]	D. Wang, S. Fu, J. Wang, Y. Li, Z. Wang, The stability degree analysis of profiles for networked evolutionary games with switching topology, Nonlinear Anal., 50 (2023), 101396. https://doi.org/10.1016/J.NAHS.2023.101396 doi: 10.1016/J.NAHS.2023.101396
[22]	G. Zhao, Y. Wang, H. Li, A matrix approach to modeling and optimization for dynamic games with random entrance, Appl. Math. Comput., 290 (2016), 9–20. https://doi.org/10.1016/j.amc.2016.05.012 doi: 10.1016/j.amc.2016.05.012
[23]	H. Li, S. Wang, W. Li, Aggregation method to strategy consensus of large-size networked evolutionary matrix games, IEEE Trans. Automat. Contr., 69 (2024), 3975–3981. https://doi.org/10.1109/tac.2023.3340558 doi: 10.1109/tac.2023.3340558
[24]	Z. Wang, S. Fu, J. Wang, X. Zhao, Strategy consensus of networked evolutionary games with time invariant delays, Dyn. Games Appl., 14 (2023), 1–16. https://doi.org/10.1007/S13235-023-00522-X doi: 10.1007/S13235-023-00522-X
[25]	D. Cheng, Y. Wu, G. Zhao, S. Fu, A comprehensive survey on STP approach to finite games, J. Syst. Sci. Complex., 34 (2021), 1666–1680. https://doi.org/10.1007/s11424-021-1232-8 doi: 10.1007/s11424-021-1232-8
[26]	G. Zhao, H. Li, P. Duan, F. Alsaadi, Survey on applications of semi-tensor product method in networked evolutionary games, J. Appl. Anal. Comput., 10 (2020), 32–54.
[27]	D. Cheng, On finite potential games, Automatica, 50 (2014), 1793–1801. https://doi.org/10.1016/j.automatica.2014.05.005
[28]	G. Zhao, X. Ma, H. Li, Construction of quasi-potential games based on topological structure, IEEE T. CIRCUITS-II, 71 (2024), 3825–3829. https://doi.org/10.1109/tcsii.2024.3371934 doi: 10.1109/tcsii.2024.3371934
[29]	J. Wang, K. Jiang, Y. Wu, On congestion games with player-specific costs and resource failures, Automatica, 142 (2022), 110367. https://doi.org/10.1016/J.AUTOMATICA.2022.110367 doi: 10.1016/J.AUTOMATICA.2022.110367
[30]	C. Li, D. Cheng, Modeling, analysis, and dynamics of Bayesian games via matrix-based method, J. Franklin Inst., 360 (2023), 6162–6193. https://doi.org/10.1016/J.JFRANKLIN.2023.04.020 doi: 10.1016/J.JFRANKLIN.2023.04.020
[31]	W. Wang, Y. Lai, Armbruster D, Cascading failures and the emergence of cooperation in evolutionary-game based models of social and economical networks, Chaos: An Int. J. Nonlinear Sci., 21 (2011). https://doi.org/10.1063/1.3621719
[32]	H. Dui, X. Meng, H. Xiao, J. Guo, Analysis of the cascading failure for scale-free networks based on a multi-strategy evolutionary game, Reliab. Eng. Syst. Saf., 199 (2020), 106919. https://doi.org/10.1016/j.ress.2020.106919 doi: 10.1016/j.ress.2020.106919
[33]	S. Fu, Y. Wang, G. Zhao, A matrix approach to the analysis and control of networked evolutionary games with bankruptcy mechanism, Asian J. Control, 19 (2017), 717–727. https://doi.org/10.1002/asjc.1412 doi: 10.1002/asjc.1412
[34]	L. Deng, S. Fu, P. Zhu, State feedback control design to avoid players going bankrupt, Asian J. Control, 21 (2019), 2551–2558. https://doi.org/10.1002/asjc.2126 doi: 10.1002/asjc.2126
[35]	H. Yuan, Z. Chen, Z. Zhang, R. Zhu, Z. Liu, Minimum-time strategy optimization for networked evolutionary games with bankruptcy mechanism, expert systems with applications, Expert Syst. Appl., 237 (2024), 121311. https://doi.org/10.1016/J.ESWA.2023.121311 doi: 10.1016/J.ESWA.2023.121311
[36]	D. Cheng, H. Qi, Z. Li, Analysis and control of Boolean networks: a semi-tensor product approach, Springer Science & Business Media, 2010.
[37]	Y. Guo, P. Wang, W. Gui, C. Yang, Set stability and set stabilization of Boolean control networks based on invariant subsets, Automatica, 61 (2015), 106–112. https://doi.org/10.1016/j.automatica.2015.08.006 doi: 10.1016/j.automatica.2015.08.006

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