Environmental-feedback-driven time-varying reputation update solve social dilemmas

The reputation mechanism serves as a critical component in sustaining the efficient functioning of social systems. Building upon existing research, this study introduces a novel time-varying reputation update rule that incorporates environmental feedback. Specifically, we establish that the reputation reward for cooperation follows a positive yet non-linear relationship with the proportion of cooperators, while the reputation penalty for defection exhibits a negative but equally non-linear correlation with the cooperator ratio. Our research yields two significant contributions: First, our findings reveal two key insights: The proposed mechanism significantly enhances cooperative behavior compared to traditional version, demonstrating superior performance in improving network reciprocity utility, and compared to homogeneous reputation, time-varying reputation update perform better in enhancing cooperation under low social dilemma. Second, we extend this framework by developing three additional time-varying reputation update rules that incorporate environmental feedback. Comparative analysis demonstrates that different reputation mechanisms exhibit varying levels of effectiveness in promoting cooperation under different intensities of social dilemmas. The reward conditions during the initial cooperative evolution will influence the spread of cooperative behavior in future systems. These findings not only deepen our theoretical understanding of reputation dynamics but also provide insights for designing context-specific reputation systems.