Good influence transmission structure strengthens cooperation in prisoner’s dilemma games

Analysis on how network reciprocity may help promote the coordination of agents in a system has attracted attention. However, designing effective methods for searching highly cooperative population structures remains a challenge. In this article, we reveal how cooperation behavior survives and spreads from a micro perspective, and further visualize the topology of influence transmission structure that supports the spread of cooperation. Based on our analysis, a highly cooperative multilevel scale-free network (mlSFNs) model is designed and compared with other existing scale-free network models. Meanwhile, we discover the positive correlation between influence coverage rate and cooperation level from a correlation analysis toward mass sample data. Thus, we introduce one rule for highly cooperative structures: influence coverage rate is essential to cooperation, while the unaffected nodes should be less influential. In our experiments, we find that this rule can provide effective guidance to the structure optimization algorithm termed fMA-CPD-SFN, which successfully optimizes various structures subject to different strategy update rules. Moreover, fMA-CPD-SFN is also applicable to the optimization of large-scale populations. In this case, we conclude that this rule is instructive for future design of a highly cooperative population structure. Graphical abstract