Zhang Liye, Zou Yong, Guan Shuguang, Liu Zonghua
Department of Physics, East China Normal University, Shanghai 200062, China.
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042807. doi: 10.1103/PhysRevE.91.042807. Epub 2015 Apr 24.
Evolutionary game theory is crucial to capturing the characteristic interaction patterns among selfish individuals. In a population of coordination games of two strategies, one of the central problems is to determine the fixation probability that the system reaches a state of networkwide of only one strategy, and the corresponding expectation times. The deterministic replicator equations predict the critical value of initial density of one strategy, which separates the two absorbing states of the system. However, numerical estimations of this separatrix show large deviations from the theory in finite populations. Here we provide a stochastic treatment of this dynamic process on complex networks of finite sizes as Markov processes, showing the evolutionary time explicitly. We describe analytically the effects of network structures on the intermediate fixations as observed in numerical simulations. Our theoretical predictions are validated by various simulations on both random and scale free networks. Therefore, our stochastic framework can be helpful in dealing with other networked game dynamics.
进化博弈论对于捕捉自私个体之间的特征性互动模式至关重要。在一个具有两种策略的协调博弈群体中，核心问题之一是确定系统达到仅一种策略全网状态的固定概率以及相应的期望时间。确定性复制方程预测了一种策略初始密度的临界值，该临界值将系统的两个吸收态分开。然而，在有限群体中，这条分界线的数值估计与理论存在很大偏差。在这里，我们将这个动态过程作为马尔可夫过程在有限规模的复杂网络上进行随机处理，明确显示出进化时间。我们通过数值模拟分析描述了网络结构对中间固定状态的影响。我们的理论预测通过在随机网络和无标度网络上的各种模拟得到了验证。因此，我们的随机框架有助于处理其他网络博弈动态。
