选择差异下Moran过程的随机博弈模型及其应用

研究有限种群中2×2的对称博弈,假设采取不同策略的个体具有不同的选择强度,建立选择差异下Moran更新过程的随机博弈模型.利用扩散近似的方法得到选择差异下Moran过程策略的扎根概率,扎根概率不仅与博弈收益矩阵和种群的大小相关,还与策略的差异选择强度相关.通过比较弱选择和中性选择下策略的扎根概率,分析自然选择有利于策略在种群中扎根及策略成为演化稳定策略的条件.在常见的三种博弈:囚徒困境,共存博弈和协调博弈中,利用数值分析方法,得到扎根概率与选择强度及种群大小之间的关系;利用仿真方法得到扎根时间与选择强度之间的关系.最后将选择差异下的Moran过程随机博弈模型,应用于解决第三方物流企业是否参与供应链金融的策略选择问题.求解第三方物流企业参与供应链金融策略的扎根概率,分析有利于参与策略扎根及参与策略成为演化稳定策略的条件,利用数值和仿真分析方法得到各参数变化对第三方物流企业博弈行为的影响.本文的研究内容扩展了Moran更新过程的随机演化博弈理论.

Stochastic evolution dynamic model of Moran process with selection difference and its application

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.