Abstract：Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy optimization for a class of multilayer evolutionary networked games with “myopic best response adjustment” rules. Firstly, the dynamics of the multilayer evolutionary networked game is converted to formulate for the game. Secondly, based on the algebraic form, the dynamic behavior of the multilayer evolutionary networked games is discussed. Finally, the strategy optimization problem is considered by adding a pseudo-player. The aim is to design optimal control sequence to maximize the average income of pseudo-players. An illustrative example shows the effectiveness of this paper.
武利琴, 王金环, 徐勇. 一种基于半张量积的多层网络演化博弈方法[J]. 复杂系统与复杂性科学, 2017, 14(3): 68-74.
WU Liqin, WANG Jinhuan, XU Yong. Multilayer Evolutionary Networked Games Base on Semi-Tensor Product. Complex Systems and Complexity Science, 2017, 14(3): 68-74.
[1] Cheng D Z, Xu T T, He F H, et al. Semi-tensor product approach to networked evolutionary games[J].Control Theory and Technology, 2014, 12(2):198204. [2]Cheng D Z, Xu T T, Qi H S. Evolutionary stability strategy of networked evolutionary games[J]. IEEE Transactions on Neural Networks and Learning Systems, 2013, 16411653. [3]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. [4]Guo P L, Wang Y Z, Li H T. Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method[J]. Automatic, 2013, 49:33843389. [5]Ge M X, Li Y, Zhao J L, et al. Strategy consensus of networked evolutionary games[J]. Journal of Shandong University(Natural Science) , 2015, 50(11):113118. [6]Du W B, Cao X B, Hu M B. The effect of asymmetric payoff mechanism on evolutionary networked prisoner’s dilemma game[J]. Physic A:Statistical Mechanic and its Application, 2009, 388(24):50055012. [7]Zhao Y, Li Z Q, Cheng D Z. Optimal control of logical control networks[J]. IEEE Transactions on Automatic Control, 2011, 56(56):17661776. [8]Wang D Z, Lang M X, Sun Y. Evolutionary game analysis of co-opetition relationship between regional logistics nodes[J].Journal of Applied Research & Technology, 2014, 12(2):251260. [9]陆君安. 从单层网络到多层网络的——结构、动力学和功能[J].统计物理和复杂系统研究前沿进展专题II, 2015, 4(27):38. Lu Junan. From single-layer network to multi-layer network-structure, dynamics and function[J]. Statistical Physics and Complex Systems Research Erontier Development TopicⅡ, 2015, 4(27):38. [10] Gao B, Deng Z H, Zhao D W. Competing spreading processes and immunization in multiplex networks[J]. Chaos, Solitons and Fractals, 2016,93:175181. [11] Wu Q C, Lou Y J, Zhu W F. Epidemic outbreak for an SIS model in multiplex networks with immunization[J].Mathematical Biosciences, 2016,277:3846. [12] Luo C, Zhang X L, Liu H, et al. Cooperation in memory-based prisoner’s dilemma game on interdependent networks[J]. PhysicA,2016, 450:560569. [13] Meng X K, Xia C Y, Gao Z K, et al. Spatial prisoner’s dilemma games with increasing neighborhood size and individual diversity on two interdependent lattices[J].Physics Letters A, 2015, 379:767773.
