Reputation-dependent social learning on the evolution of cooperation in spatial public goods games

In this study, we propose a new second-order reputation evaluation rule in the spatial public goods games, in which both actions of the individual and his neighbors with the worst reputation are taken into account. Considering the incomplete accessibility of individual reputation information, we introduce a reputation reasoning ability parameter and study the effect of reputation on individual strategy updating from the perspective of social learning, in which individuals with large reputation reasoning abilities are more likely to choose neighbors with a high reputation for strategy imitation. Three cases where the reputation reasoning ability parameter is homogeneous, endogenous, and exogenous are considered and compared. From simulation results, we find that high reputation reasoning ability can promote cooperation in all cases. Specifically, in the homogeneous reputation reasoning ability situation, compared with the first-order rules, the secondorder information on reputation inhibits cooperation rather than promotes it and a significant magnitude of reputation change can also inhibit cooperation. In endogenous situations where reasoning ability is negatively correlated with individual reputation, large correlation coefficients can inhibit cooperation. In exogenous situations of the normal distribution, a high mean of reputation reasoning ability boosts cooperation, but when the variance is sufficiently large, the level of cooperation will no longer be affected. In scenarios of the power law distribution, the cooperation level improves with an increase in the power index. These findings further expand our understanding of high-order reputation evaluation rules in multiplayer games and incomplete reputation information environment on the evolution of cooperation from the perspective of reputation-dependent social learning.