Reputation-based conditional compassion promotes cooperation in spatial public goods games

Compassion, as a typical altruistic social preference, can explain the phenomenon of cooperation to a certain extent. However, compassion is conditional in reality, and it can only be triggered under certain conditions. Based on this observation, we introduce a kind of reputation-based compassion mechanism in spatial public goods games. We set a proportion of individuals in the population as being compassionate, and only individuals with relatively low payoffs and not too low reputations may receive sympathy from other individuals who are compassionate in the group. We find that compared with randomly selecting individuals who are compassionate, individuals in the top rank of payoff or reputation being compassionate are more likely to promote cooperation; in this case, even if one percent of individuals in the population are compassionate, the level of cooperation can be significantly improved. The higher the payoff redistribution ratio, the higher the cooperative rate in the population. By classifying individuals and comparing their payoffs before and after compassion, we find that most of the payoff redistribution occurs at the boundary of the cooperator clusters. The reduction of payoff gaps affects the strategy imitation, that is, the possibility of low-payoff individuals imitating the strategies of high-payoff individuals can be increased. These results expand our understanding of conditional compassion in promoting cooperation.