A game-theoretical model is constructed to capture the effect of imitation on the evolution of cooperation. This imitation describes the case where successful individuals are more likely to be imitated by newcomers who will employ their strategies and social networks. Two classical repeated strategies ‘always defect (ALLD)’ and ‘tit-for-tat (TFT)’ are adopted. Mathematical analyses are mainly conducted by the method of coalescence theory. Under the assumption of a large population size and weak selection, the results show that the evolution of cooperation is promoted in this dynamic network. As we observed that the critical benefit-to-cost ratio is smaller compared to that in well-mixed populations. The critical benefit-to-cost ratio approaches a specific value which depends on three parameters, the repeated rounds of the game, the effective strategy mutation rate, and the effective link mutation rate. Specifically, for a very high value of the effective link mutation rate, the critical benefit-to-cost ratio approaches 1. Remarkably, for a low value of the effective link mutation rate, by letting the effective strategy mutation is nearly equal to zero, the critical benefit-to-cost ratio approaches \(1+\frac{1}{m-1}\) for the resulting highly connected networks, which allows TFT to be evolutionary stable. It illustrates that dominance of TFTs is associated with more connected networks. This research can enrich the theory of the coevolution of game strategy and network structure with dynamic imitation.

建立了博弈论模型来捕捉模仿对合作演变的影响。这种模仿描述了成功人士更容易被采用其策略和社交网络的新人模仿的情况。采用了两种经典的重复策略“总是缺陷（ALLD）”和“针锋相对（TFT）”。数学分析主要通过合并理论的方法进行。在人口众多且选择不力的假设下，结果表明在这个动态网络中促进了合作的发展。正如我们观察到的那样，关键收益/成本比比充分混合的人群要小。关键的成本收益比接近一个特定的值，该值取决于三个参数：游戏的重复轮次，有效策略突变率和有效链接突变率。具体来说，对于有效链接突变率的非常高的值，关键的成本效益比接近1。值得注意的是，对于有效链接突变率的低值，通过使有效策略突变几乎等于零，关键的成本效益比方法\（1+ \ frac {1} {m-1} \）用于生成高度连接的网络，这使TFT能够保持进化的稳定性。它说明了TFT的优势与更多连接的网络相关联。该研究可以通过动态模仿丰富博弈策略与网络结构协同进化的理论。