Abstract：The evolutionary congestion game with attackers and feasible state constrained set is investigated, using the semi-tensor product method of matrix, game dynamic system is transformed into an algebraic form and studied its robustness. Firstly, evolutionary congestion game with attackers and controllers is transformed into an algebraic form. Secondly, the open-loop control and state feedback control are transformed, and the Nash equilibrium is robust for any initial profiles in the restricted set of feasible states. Finally, an example is presented to illustrate that the dynamic system of evolutionary congestion game with attackers can achieve robust reachable equilibrium under open-loop control and state feedback control.
王桂林, 徐勇. 带攻击玩家的演化拥塞博弈的鲁棒性分析[J]. 复杂系统与复杂性科学, 2020, 17(2): 47-53.
WANG Guilin, XU Yong. Robustness Analysis of Evolutionary Congestion Game with Attackers. Complex Systems and Complexity Science, 2020, 17(2): 47-53.
[1]Rosenthal R W. A class of games possessing pure-strategy Nash equilibriam[J]. International Journal of Game Theory, 1973, 2(1): 6567. [2]Imane D B, Abdelfettah M. 5G-dynamic resource sharing mechanism for vehicular networks: congestion game approach[C]. International Symposium on Advanced Electrical and Communication Technologies (ISAECT), 2018: 15. [3]Tatsuya I, Yukihiro T, Daisuke F. Self-fulfilling signal of an endogenous state in network congestion games[J]. Networks and Spatial Economics, 2017, 17(3): 889909. [4]刘觉夫, 陈晓. 基于空间拥塞博弈的自适应负载频谱算法研究[J]. 计算机工程与科学, 2013, 35(7): 6470. Liu Juefu, Chen Xiao. Research on adaptive load spectrum algorithms based on spatial congestion game[J]. Computer Engineering and Science, 2013, 35(7): 6470. [5]王祖喜, 邓昭彰, 李力. 基于局域信息少数者博弈的拥塞控制算法[J]. 通信学报, 2014, 35(1): 148166. Wang Zhuxi, Deng Zhaozhang, Li Li. Congestion control algorithm based on local information minority game[J]. Journal of Communications, 2014, 35(1): 148166. [6]Marden J R, Wierman A. Distributed welfare games[J]. Operations Research, 2013, 61(1): 155168. [7]Wang Y H, Cheng D Z. Stability and stabilization of a class of finite evolutionary games[J]. Journal of the Franklin Institute, 2017, 354(3): 16031617. [8]Fu S H. Modeling, analysis and optimization of a type of evolutionary public goods games[C]. Chinese Automation Congress, Jinan, China, 2017. [9]Cheng D Z, He F H, Qi H S, et al. Modeling, analysis and control of networked evolutionary games[J]. IEEE Transactions on Automatic Control, 2015, 60(9): 24022415. [10] Mao Y, Wang L Q, Liu Y, et al. Stabilization of evolutionary networked games with length-r information[J]. Applied Mathematics and Computation, 2018, 377: 442451. [11] Fu S H, Zhao G D, Li H T, et al. Model and control for a class of networked evolutionary games with finite memories and time-varying networks[J]. Circuits Systems and Signal Processing, 2018, 37(7): 30933114. [12] Zhao G D, Li H T, Sun W W, et al. Modelling and strategy consensus for a class of networked evolutionary games[J]. Journal International Journal of Systems Science, 2018, 49(12): 25482557. [13] Zhang K Z, Xiao N, Xie L H. Convergence speed analysis for evolutionary congestion games[C]. The 10th Asian Control Conference, Kota Kinabalu, 2015: 15. [14] Hao Y Q, Pan S S, Qiao Y P, et al. Cooperative control via congestion game approach[J]. IEEE Transactions on Automatic Control, 2016, 63(12): 18. [15] Zhong J, Liu Y, Kou K I. On the ensemble controllability of Boolean control networks using STP method[J]. Applied Mathematics and Computation, 2019, 358: 5162. [16] Liu H C, Liu Y, Li Y Y. Observability of Boolean networks via STP and graph methods[J]. IET Control Theory and Applications, 2019, 13(7): 10311037. [17] Liu R J, Lu J Q, Liu Y, et al. Delayed feedback control for stabilization of Boolean control networks with state delay[J]. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(7): 3283 3288. [18] Yu Y Y, Meng M, Feng J E, et al. Stabilizability analysis and switching signals design of switched Boolean networks[J]. Nonlinear AnalysisHybrid Systems. 2018, 30: 3144. [19] Sylvain C,Satoru T. Robustness to incomplete information in repeated games[J]. Theoretical Economics, 2011, 6: 4993. [20] Zhang X, Hao Y Q, Cheng D Z. Incomplete potential game[C]. Proceedings of the 36th Chinese Control Conference, Dalian, China, 2017. [21] Li B W, Lu J Q, Liu Y. The local convergence of boolean networks with disturbances[J]. IEEE Transactions on Circuits and Systems II-Express Briefs, 2019, 66(4): 667671. [22] Li B W, Liu Y, Lou J G, et al. The robustness of outputs with respect to disturbances for boolean control networks[J]. IEEE Transactions on Neural Networks and Learning Systems, 2019: 16. [23] Li Y L, Ding X Y, Li H T. Robust consensus of networked evolutionary games with attackers and forbidden profiles[J]. Entropy, 2018: 113. [24] Cheng D Z, Qi H S. Analysis and Control of Boolean Networks: A Semi-tensor Product Approach[M]. London: Springer, 2011. [25] John F N . Non-cooperative game[J]. The Annals of Mathematics, 1951, 54(2): 286295.
