Environmental feedback mechanism coupling reputation and node entropy in spatial public goods games

Cooperation in public goods games is strongly affected by the interaction between individual behavior, social evaluation, and the surrounding payoff environment. To capture this interplay, this study develops a spatial public goods game model with an endogenous environmental feedback mechanism jointly regulated by reputation and node entropy. In the proposed framework, reputation serves as a dynamic measure of social evaluation shaped by individual behavior, while node entropy is introduced to characterize the strength of local behavioral inclination and the heterogeneity of the surrounding interaction environment. Based on weighted local reputation and weighted local node entropy, the synergy factor is no longer treated as a fixed parameter, but adaptively adjusted through a feedback rule, allowing the payoff environment to evolve with local social conditions. In addition, strategy updating incorporates both payoff comparison and reputation comparison, thereby reflecting a decision process influenced by material incentives as well as social information. Through this construction, the model establishes a closed coevolutionary loop among strategy, reputation, node entropy, and environmental feedback. The results show that endogenous environmental feedback can create favorable conditions for the persistence of cooperation, while its effectiveness depends on the updating mechanism and the structure of the baseline reputation distribution. The proposed model provides a new perspective for understanding how social evaluation, local heterogeneity, and adaptive environments jointly shape the evolution of cooperation in spatial social dilemmas.