Reputation evaluation with tolerance and reputation-dependent imitation on cooperation in spatial public goods game

Reputation exists widely in human society and plays a significant role in people's behavioral norms. People with a good reputation are more likely to be noticed in society, so their behaviors are more likely to be imitated and spread. However, traditional imitation models in evolutionary games based on the Fermi rule ignore this reality. Based on this observation, this paper improves the existing spatial public goods game models in two aspects. First, we introduce a reputation evaluation mechanism considering tolerance, allowing individuals to defect in a harsh environment in which the number of detected neighbors in the group is large whereas not affecting their reputation. Moreover, different from the traditional random selection of neighbors as imitation objects in the process of individual strategy evolution, this paper assumes that individuals with a good reputation have a higher probability of being selected, whereas whether to imitate this individual depends on the Fermi function based on the payoff difference. Through simulation experiments, we found that reputation-dependent imitation can improve the cooperation level of the population. We also found that small values of tolerance in reputation evaluation provide a better environment for the survival of cooperators. This mechanism allows us to better understand the pervasive phenomenon of cooperation in the social system.