Based on a continuous mixed strategy game model considering the memory mechanism and the uncertainty of individual decision-making, we explore the influence of several different update rules on the spatial cooperation behavior. Here, we mainly investigate the role of the Moran-like process, Fermi rule and replicator dynamics in the evolution of cooperation. Meanwhile, we further compare the evolution of cooperation when the memory mechanism and individual uncertainty are taken into account. In particular, memory length M and strategy adjustment factor \(\delta \) can promote the cooperation behavior in different ways. Extensive Monte Carlo simulations indicate that the Moran-like process can generally drive the expansion of cooperative clusters faster and finally achieve the highest frequency of cooperation although the Fermi update rule performs better under the same condition. Moreover, the replicator dynamics create the worst scenario as far as the evolution of cooperation is concerned. Therefore, the level of cooperation strongly depends on the strategy update rules; these findings may be helpful to understand and analyze the evolutionary process of cooperation in many real-world natural and social systems.

基于考虑了记忆机制和个体决策不确定性的连续混合策略博弈模型，我们探讨了几种不同的更新规则对空间合作行为的影响。在这里，我们主要研究莫兰式过程，费米法则和复制者动力学在合作演变中的作用。同时，我们进一步比较了考虑记忆机制和个体不确定性时合作的演变。特别是，内存长度M和策略调整因子\（\ delta \）可以以不同的方式促进合作行为。广泛的蒙特卡洛模拟表明，尽管在相同条件下费米更新规则的执行效果更好，但类似Moran的过程通常可以更快地推动合作集群的扩展并最终达到最高的合作频率。而且，就合作的发展而言，复制者的动态创造了最坏的情况。因此，合作水平在很大程度上取决于策略更新规则。这些发现可能有助于理解和分析许多现实世界中自然和社会系统中合作的进化过程。