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中国物理学会期刊

空间囚徒困境中迁移感知半径与博弈交互半径的变化对合作演化的影响

Effects of migration perceptual radius and game interaction radius on cooperation evolution in spatial prisoner's dilemma

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  • 在自然界与人类社会中,个体的空间移动决策与博弈交互半径往往受到不同机制的支配.本文将迁移感知半径与博弈交互半径作为两个相互独立的参数,构建了可连续迁移的囚徒困境模型,系统研究了二者的变化对合作演化的影响机制.研究发现,迁移感知半径对合作水平具有非单调的调控作用:感知半径过小时,个体迁移缺乏方向引导,合作者难以有效聚集;感知半径处于特定中间值时,背叛者能够高效追踪并瓦解合作者的局部聚集,导致合作水平出现显著谷值;而当感知半径增大至适中水平后,合作者得以实现定向聚集,建立起稳定的结构性防护,合作水平因此大幅提升;感知半径继续增大则因大量背叛者跟随而导致合作再度衰退.进一步研究表明,迁移步长,背叛诱惑参数与博弈交互半径均会对上述规律产生一定影响.此外,群体密度对合作演化的影响则呈现单峰结构,低密度下大感知半径对合作的促进效果尤为突出,高密度则普遍抑制合作.本文结果为理解现实复杂系统中个体移动行为促进合作涌现的内在机制提供了新的理论视角.

     

    In nature and human society, individuals' spatial movement decisions and game interaction ranges are often governed by distinct mechanisms. However, most previous studies on evolutionary game dynamics with migration have defaulted to treating the game interaction radius and migration perceptual radius as identical, which ignores the prevalent range asymmetry between strategic interaction and spatial movement in real systems. In this paper, we decouple these two radii by treating the migration perceptual radius r_\rm m and game interaction radius r_\rm i as two fully independent parameters, construct a spatial prisoner's dilemma model with continuous migration in two-dimensional continuous space, and investigate how variations in these two factors affect the evolution of cooperation through numerical simulations and microscopic mechanism analysis. We find that the migration perceptual radius exerts a pronounced non-monotonic regulatory effect on the cooperation level. When r_\rm m is excessively small, individuals lack directional guidance for migration, making it difficult for cooperators to aggregate effectively, and the cooperation level remains close to that of random mixing. When r_\rm m lies within a specific intermediate range, defectors can efficiently track and infiltrate local cooperator clusters, leading to a pronounced valley in the cooperation level that is robust across a wide range of parameter combinations including different values of the temptation to defect and game interaction radii. In contrast, when r_\rm m increases to a moderate level, cooperators achieve directed aggregation and form stable structural protection against defector invasion, resulting in a substantial enhancement of cooperation. A further increase in r_\rm m enables defectors to follow cooperators' movement signals at large scale, breaking cooperative clusters and causing the cooperation level to decline again. Through snapshots of spatial distributions and polar rose diagrams of migration directions, we reveal the microscopic mechanisms underlying each regime. Furthermore, the game interaction radius r_\rm i plays a key regulatory role in cooperation evolution. An intermediate r_\rm i most effectively supports the formation and maintenance of cooperative clusters, while an excessively large r_\rm i weakens network reciprocity and suppresses cooperation. In the parameter space spanned by r_\rm i and r_\rm m, the cooperation level exhibits a clearly non-uniform distribution with sharp boundaries between high-cooperation and low-cooperation regions, confirming the significant joint regulatory roles of both radii. In addition, the migration step size and population density interact with r_\rm m to jointly determine cooperation outcomes. The promoting effect of an optimal r_\rm m is particularly prominent at low population density, whereas high density generally suppresses the cooperation level. These results provide a novel theoretical perspective for understanding the intrinsic mechanisms by which individual movement behaviors facilitate the emergence of cooperation in real-world complex systems.

     

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