The evolution of cooperation is a pivotal area of study, essential for understanding the survival and success of complex biological and social systems. This paper investigates the dynamics of cooperation in spatial public goods games (SPGG) through a model that incorporates a fairness-driven migration mechanism. In this model, agents move towards environments perceived as fairer, influencing the spatial distribution and overall level of cooperation within the population. We examine the interplay between the time scale ratio, noise in movement, and population density. Our analysis reveals that moderate levels of movement and noise are critical for forming and maintaining cooperative clusters, while excessive movement and noise disrupt these structures, leading to reduced cooperation. Higher enhancement factors increase the resilience of cooperative behavior, extending the range of movement intensity over which high cooperation levels are maintained. Population density significantly impacts cooperative dynamics, with high-density environments promoting the coexistence of cooperators and defectors but lowering the highest achievable cooperation levels due to increased exploitation. Our findings underscore the importance of balancing movement, noise, and density to sustain cooperation and stable social structures. This research provides valuable insights for designing interventions and policies to promote cooperative behavior and social cohesion in complex populations. Future studies should further explore the adaptive mechanisms that dynamically adjust movement and strategy adaptation based on local environmental conditions.

中文翻译：

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空间公共产品博弈中公平寻求主体之间合作的演变


合作的演变是一个关键的研究领域，对于理解复杂的生物和社会系统的生存和成功至关重要。本文通过一个包含公平驱动迁移机制的模型来研究空间公共产品博弈 （SPGG） 中的合作动态。在这个模型中，代理们朝着被认为更公平的环境前进，从而影响人口内部的空间分布和整体合作水平。我们研究了时间尺度比率、运动中的噪声和人口密度之间的相互作用。我们的分析表明，适度的运动和噪声对于形成和维持协作集群至关重要，而过度的运动和噪声会破坏这些结构，导致合作减少。较高的增强因子增加了合作行为的弹性，扩大了保持高合作水平的运动强度范围。人口密度显著影响合作动态，高密度环境促进了合作者和叛逃者的共存，但由于剥削的增加，降低了可实现的最高合作水平。我们的研究结果强调了平衡运动、噪音和密度以维持合作和稳定社会结构的重要性。这项研究为设计干预措施和政策以促进复杂人群的合作行为和社会凝聚力提供了有价值的见解。未来的研究应进一步探索根据局部环境条件动态调整运动和策略适应的适应机制。