超越公地悲剧的合作演化:环境反馈演化博弈动力学综述与展望
Evolution of cooperation beyond the tragedy of the commons:A review of evolutionary game dynamics with environmental feedback
摘要
Abstract
This paper systematically reviews recent advances in evolutionary game dynamics with environmental feedback,a theoretical framework characterizing the continuous coevolution of individual strategies and environmental states.First,under the mean-field approximation,we detail models that couple replicator dynamics with environmental variables,especially frameworks in which payoff structures are coupled to environmental states.We summarize the research on rigorous conditions for the"oscillatory tragedy of the commons"(o-TOC)and explain how physical and ecological factors—such as finite carrying capacity,mutation,fluctuation,and time delays—can induce bifurcations(e.g.,Hopf bifurcations),multistability,and oscillations,thereby reshaping the phase portrait and the conditions under which"tragedy of the commons(TOC)"outcomes emerge or can be averted.Furthermore,we outline how integrating explicit common-resource governance mechanisms,such as state-dependent inspection and punishment,compensation,and other incentive mechanisms,can steer the nonlinear system away from resource depletion.Second,we introduce the effects of spatial structures and network topologies.The transition from well-mixed populations to localized interactions and resource diffusion can break global synchronization,leading to the formation of self-organized spatiotemporal patterns and strategy-resource clusters.We highlight two coupled mechanisms:cooperator clustering can enhance local payoffs and environmental recovery,while localized feedback reshapes cluster-boundary stability,thereby reshaping invasion and coexistence dynamics and transition pathways.Third,we discuss game state transitions as a discrete environmental feedback framework,where collective actions trigger payoff changes,highlighting how asymmetric returns across discrete states facilitate cooperation.Finally,we bridge frontier empirical findings with theoretical studies,explicitly discussing microbial public-goods experiments(where public goods reshape competitor metabolism)and real-world resource governance.We conclude by outlining future research directions,particularly the necessity of incorporating multiscale heterogeneous resources,complex mechanisms of real-world social and ecological systems,collective decision-making mechanisms,finite-population stochasticity,and the direct coupling of environmental feedback to demographic processes such as survival and reproduction.Overall,this review clarifies the major frontiers and developmental trajectory of evolutionary games with environmental feedback,and offers a reference for understanding the emergence of cooperation and the regulation of TOC phenomena.关键词
复杂系统/演化博弈/环境反馈/合作演化Key words
complex systems/evolutionary games/environmental feedback/evolution of cooperation引用本文复制引用
陈奕多,吴枝喜,关剑月..超越公地悲剧的合作演化:环境反馈演化博弈动力学综述与展望[J].物理学报,2026,75(17):1-9,9.基金项目
国家自然科学基金(批准号:12575039,12375032,12247101)、中央高校基本科研业务费(批准号:lzujbky-2025-it50,lzujbky-2024-11,lzujbky-2024-jdzx06,lzujbky-2023-ey02)、甘肃省教育厅高校研究生"创新之星"项目(批准号:2026CXZX-153)、甘肃省自然科学基金(批准号:22JR5RA389)、高等学校学科创新引智计划(批准号:B20063)和甘肃省陇原青年英才项目资助的课题. Project supported by the National Natural Science Foundation of China(Grant Nos.12575039,12375032,12247101),the Fundamental Research Funds for the Central Universities,China(Grant Nos.lzujbky-2025-it50,lzujbky-2024-11,lzujbky-2024-jdzx06,lzujbky-2023-ey02),the 2026 Graduate Innovation Star Project of Gansu Provincial Department of Education,China(Grant No.2026CXZX-153),the Natural Science Foundation of Gansu Province,China(Grant No.22JR5RA389),and the 111 Center(Grant No.B20063),and the Longyuan-Youth-Talent Project of Gansu Province,China. （批准号:12575039,12375032,12247101）
