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The reciprocal influence between the environment and the cooperation level is a ubiquitous reality. Changes in cooperation levels impact environmental quality, while environmental conditions, in turn, affect individual fitness and behavior. Drawing inspiration from this inherent interplay, we investigate the role of environmental feedback on the spatial prisoner's dilemma game. We establish two discrete environmental states by introducing a feedback parameter. Furthermore, we incorporate a more realistic scenario wherein individuals with higher fitness are more likely to be imitated by their neighbors due to preferential selection. Our findings reveal that environmental feedback efficiently fosters cooperation, driven by the preferential selection. Moreover, a specific parameter range is identified in which the enhancement for cooperation is most pronounced. Notably, we observe that environmental feedback alone does not enhance cooperation, a result potentially linked to the nature of feedback formulations employed. These results provide valuable insights into the emergence and evolution of cooperation within complex systems. • Environmental feedback efficiently promotes cooperation in the spatial prisoner's dilemma game, stimulated by the preferential selection mechanism. • There exists the optimal combination of environmental feedback ( δ ) and preferential selection ( α ) that maximizes the level of cooperation. • The environmental feedback alone has no influence on cooperation, which is potentially linked to the nature of feedback forms employed. While preferential selection alone has a positive effect on cooperation.
Li et al. (Fri,) studied this question.