Games with environmental feedback have become a crucial area of study across various scientific domains, modelling the dynamic interplay between human decisions and environmental changes, and highlighting the consequences of our choices on natural resources and biodiversity. In this work, we propose a co-evolutionary model for human-environment systems that incorporates the effects of knowledge feedback and social interaction on the sustainability of common pool resources. The model represents consumers as agents who adjust their resource extraction based on the resource's state. These agents are connected through social networks, where links symbolize either affinity or aversion among them. The interplay between social dynamics and resource dynamics is explored, with the system's evolution analyzed across various network topologies and initial conditions. We find that knowledge feedback can independently sustain common pool resources. However, the impact of social interactions on sustainability is dual-faceted: it can either support or impede sustainability, influenced by the network's connectivity and heterogeneity. A notable finding is the identification of a critical network mean degree, beyond which a depletion/repletion transition parallels an absorbing/active state transition in social dynamics, i.e., individual agents and their connections are/are not prone to being frozen in their social states. Furthermore, the study examines the evolution of the social network, revealing the emergence of two polarized groups where agents within each community have the same affinity. Comparative analyses using Monte-Carlo simulations and rate equations are employed, along with analytical arguments, to reinforce the study's findings. The model successfully captures how information spread and social dynamics may impact the sustanebility of common pool resource.

翻译：具有环境反馈的博弈已成为跨学科研究的关键领域，用于模拟人类决策与环境变化之间的动态交互，揭示人类选择对自然资源和生物多样性的深远影响。本文提出一种人地系统协同演化模型，融合知识反馈与社会互动对公共池资源可持续性的作用机制。该模型将消费者建模为根据资源状态调整提取行为的智能体，这些智能体通过社会网络相互连接，其中连边表征智能体间的亲疏关系。我们探究了社会动态与资源动态的交互作用，系统分析了不同网络拓扑结构与初始条件下的演化过程。研究发现，知识反馈可独立维持公共池资源的可持续性，但社会互动对可持续性的影响具有双重性：网络连通性与异质性既能促进也可能阻碍可持续性。关键发现是识别出网络平均度的临界值——当超越该阈值时，资源枯竭/恢复相变与社会动力学中的吸收/活跃态相变同步发生，即个体智能体及其连接不再（或倾向于）固化于社会状态。此外，研究揭示了社会网络演化中极化群体的涌现：同一社群内智能体呈现相同亲缘取向。我们采用蒙特卡洛模拟、速率方程及解析论证的多维比较分析强化研究结论。该模型成功捕捉了信息传播与社会动态对公共池资源可持续性的影响机制。