Promotion of cooperation in a structured population with environmental feedbacks

Cooperation is a representative altruistic behavior in which individuals contribute public goods to benefit their neighborhoods and even larger communities in social networks. The defective behavior is more likely to bring higher payoffs than the cooperative behavior, which makes the cooperative behavior hard to maintain and sustain. Many mechanisms were proposed to promote cooperation within a social dilemma, in which some recent studies introduced the impact of dynamically changing environments on players' payoffs and strategies in social-ecological systems, and evolutionary-ecological systems. However, degree heterogeneity, an important structural property of many real-world complex networks such as social networks, academic collaboration networks, and communication networks, is rarely explored and studied in such eco-evolutionary games. In this research, we propose a Public Goods Game model on social networks with environmental feedback and analyze how the environmental factor and network structure affect the evolution of cooperation. It is found that as the initial environmental factors and the cooperation-enhancement defection-degradation ratio increase, the steady cooperation level of the social network significantly increases, and the dynamic environment will eventually evolve into a high-return environment; On the other hand, even if the initial environmental benefit coefficient is high, when the cooperation-enhancement defection-degradation ratio is less than a threshold, the dynamic environment will gradually degrade into a low-return environment. The steady cooperation level of the social network first gradually increases as the network structure becomes more heterogeneous, but it will decrease once the heterogeneity of the social network exceeds a certain threshold.