The evolution of cooperation is studied within the context of an evolutionary snowdrift game on three special networks chosen to have the same uniform degree but with different extents of spatial correlations. The cooperative behaviors on the networks differ in where the phase transitions take place and the frequencies of cooperation in the mixed phase. With only the spatial correlations being different, the study allows us to gauge the accuracy of different theoretical approaches and shed light on the choice of theoretical approaches in handling spatial correlations. It is found that analyzing the last surviving patterns often provides an understanding in the transitions in the cooperative behavior. We also construct a theoretical framework to describe the dynamical process. For different approaches of incorporating the agents’ spatial correlations, the local configuration approximation captures all the features observed in numerical simulations, while the commonly used pair approximation is too crude for quantitative purposes in studying cooperation, especially on networks with more complicated spatial correlations.

在进化雪堆游戏的背景下，在三个具有相同统一程度但空间相关程度不同的特殊网络上研究了合作的演化。网络上的协作行为在相变发生的位置和混合阶段的协作频率方面有所不同。在仅空间相关性不同的情况下，本研究允许我们评估不同理论方法的准确性，并阐明处理空间相关性的理论方法的选择。结果发现，分析最后的生存模式通常可以提供对合作行为转变的理解。我们还构建了描述动力学过程的理论框架。