Diverse selection intensities resolve the cooperation dilemma induced by breaking the symmetry between interaction and learning

Traditionally, the evolution of cooperation on structured population assumed the uniform interaction partner between gaming and learning. Yet in real-world society, individuals often act different roles in which environments gaming partners differ from learning partners. This investigation studies the evolution of cooperation under the effects of the diverse selection intensity induced by network asymmetry on two-layer networks, where the gaming and learning environments are modeled by different layers, respectively. It is found that heterogeneous selection intensity can alleviate the cooperation dilemma induced by asymmetry between gaming and learning environments. When selection intensity has a correlation with the edge overlap level of two layers, it is found that both positive correlation and negative correlation can optimize the evolution of cooperation for a moderate overlap level. However, positive correlation performs better than negative correlation in promoting the evolution of cooperation. Moreover, the increasing heterogeneity of selection enhances the evolution of cooperation under positive correlation, yet has different effects on cooperation under negative correlation for different temptations. Furthermore, we prove that the results are robust to the deterministic learning process as well as a higher noise.