Multiplicative noise enhances spatial reciprocity

Recent research has identified the heterogeneity as crucial for the evolution of cooperation in spatial population. However, the influence of heterogeneous noise is still lacking. Inspired by this interesting question, in this work, we try to incorporate heterogeneous noise into the evaluation of utility, where only a proportion of population possesses noise, whose range can also be tuned. We find that increasing heterogeneous noise monotonously promotes cooperation and even translates the full defection phase (of the homogeneous version) into the complete cooperation phase. Moreover, the promotion effect of this mechanism can be attributed to the leading role of cooperators who have the heterogeneous noise. These type of cooperators can attract more agents penetrating into the robust cooperator clusters, which is beyond the text of traditional spatial reciprocity. We hope that our work may shed light on the understanding of the cooperative behavior in the society.