Stochastic evolution dynamic model of Moran process with selection difference and its application
WANG Xianjia1,2, GU Cuiling2, ZHAO Jinhua1, HE Qilong3
1. School of Economics and Management, Wuhan University, Wuhan 430072, China; 2. Institute of Systems Engineering, Wuhan University, Wuhan 430072, China; 3. Business School, Zhengzhou University, Zhengzhou 450001, China
Abstract：We studied 2×2 symmetric games of finite population in which individuals who choose different strategies have different selection intensities. The frequency-dependent Moran process with different selection intensities was established and the fixation probability of each strategy was obtained by diffusion approximation under weak selection. The fixation probability is not only related to the population size and game matrix, but also to the differential selection intensities. The conditions that natural selection is beneficial to the fixation of strategies and that the evolutionary stability strategy ( ESS_N) satisfies were analyzed by comparing the fixation probability with that under neutral selection. In prisoner's dilemma, coexistence and coordination games, the relationships between the fixation probabilities and the selection intensities and population size were obtained by numerical analysis, and the relationships between fixation time and different selection intensities were obtained by simulation analysis. Finally, the stochastic evolution dynamic model of Moran process with selection difference was applied to the problem of strategic evolution of third party logistics enterprises. The fixation probability that the third party logistics enterprises choose to participate supply chain finance and the conditions under which the participation strategy becomes an evolutionary stable strategy were obtained. The influence of each parameter on the game behavior of the third party logistics enterprises were analyzed by numerical analysis or simulation analysis. Our research enriches stochastic evolutionary game theory based on the Moran Process.
王先甲, 顾翠伶, 赵金华, 何奇龙. 选择差异下Moran过程的随机博弈模型及其应用[J]. 系统工程理论与实践, 2020, 40(5): 1193-1209.
WANG Xianjia, GU Cuiling, ZHAO Jinhua, HE Qilong. Stochastic evolution dynamic model of Moran process with selection difference and its application. Systems Engineering - Theory & Practice, 2020, 40(5): 1193-1209.
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2020, Vol. 40 
