Coevolutionary game dynamics with localized environmental resource feedback

arXiv - QuanBio - Populations and Evolution Pub Date : 2024-07-26 DOI:arxiv-2407.18494

Yi-Duo ChenLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China, Jian-Yue GuanLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China, Zhi-Xi WuLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China

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Abstract

Dynamic environments shape diverse dynamics in evolutionary game systems. We introduce spatial heterogeneity of resources into the Prisoner's Dilemma Game model to explore the co-evolution of individuals' strategies and environmental resources. The adequacy of resources significantly affects the survival competitiveness of surrounding individuals. Feedback between individuals' strategies and the resources they can use leads to the dynamic of the "oscillatory tragedy of the commons". Our findings indicate that when the influence of individuals' strategies on the update rate of resources is significantly high, individuals can form sustained spatial clustered patterns. These sustained patterns can directly trigger a transition in the system from the persistent periodic oscillating state to an equilibrium state. These findings align with observed phenomena in real ecosystems, where organisms organize their spatial structures to maintain system stability. We discuss critical phenomena in detail, demonstrating that the aforementioned phase transition is robust across various system parameters including: the strength of cooperators in restoring the environment, the initial distributions of cooperators, and noise.

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具有局部环境资源反馈的协同进化博弈动力学

动态环境塑造了进化博弈系统中的各种动态。我们将资源的空间异质性引入囚徒困境博弈模型，探讨个体策略与环境资源的共同演化。资源的充足与否会极大地影响周围个体的生存竞争力。个体策略与可利用资源之间的反馈导致了 "振荡型公地悲剧 "的动态发展。我们的研究结果表明，当个体策略对资源更新率的影响显著较高时，个体可以形成持续的空间集群模式。这些发现与在真实生态系统中观察到的现象相吻合，在真实生态系统中，生物通过组织空间结构来维持系统的稳定性。我们详细讨论了临界现象，证明上述相位转换在各种系统参数下都是稳健的，这些参数包括：合作者恢复环境的强度、合作者的初始分布和噪声。

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arXiv - QuanBio - Populations and Evolution

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