Cooperation can emerge in the co-evolution of the local environments

Explaining the emergence of cooperation is a challenging issue. Recently, research on ecological evolutionary games has combined human behavior with environmental feedback, demonstrating that the co-evolution of cooperation and the environment exhibits rich dynamics, thereby attracting widespread attention. In this work, we aim to extend the theory of environmental feedback by exploring environmental evolution that incorporates spatial factors. Our model considers the context of a local environment, where an individual's environment is influenced only by herself and her neighbors, and the environment affects only the outcome of the game interactions in which she participates. By means of Monte Carlo simulations, our results suggest that cooperation can emerge in the co-evolution of local environments and can be facilitated more effectively with a higher degree of maximum possible environmental degradation. In particular, we discovered that environmental degradation of peripheral individuals in cooperative clusters reduces the profits of defectors, acting as a shield to protect clusters from defectors. However, in a more easily recoverable environment, this protective effect weakens, allowing free-riders to take advantage. Our research elucidates the co-evolutionary process within local environments and emphasizes the crucial role of environmental feedback in the evolution of cooperation.