Wang Zhen, Kokubo Satoshi, Tanimoto Jun, Fukuda Eriko, Shigaki Keizo
Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong and Center for Nonlinear Studies, the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, Hong Kong.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Oct;88(4):042145. doi: 10.1103/PhysRevE.88.042145. Epub 2013 Oct 29.
Up to now, there have been a great number of studies that demonstrate the effect of spatial topology on the promotion of cooperation dynamics (namely, the so-called "spatial reciprocity"). However, most researchers probably attribute it to the positive assortment of strategies supported by spatial arrangement. In this paper, we analyze the time course of cooperation evolution under different evolution rules. Interestingly, a typical evolution process can be divided into two evident periods: the enduring (END) period and the expanding (EXP) period where the former features that cooperators try to endure defectors' invasion and the latter shows that perfect C clusters fast expand their area. We find that the final cooperation level relies on two key factors: the formation of the perfect C cluster at the end of the END period and the expanding fashion of the perfect C cluster during the EXP period. For deterministic rule, the smooth expansion of C cluster boundaries enables cooperators to reach a dominant state, whereas, the rough boundaries for stochastic rule cannot provide a sufficient beneficial environment for the evolution of cooperation. Moreover, we show that expansion of the perfect C cluster is closely related to the cluster coefficient of interaction topology. To some extent, we present a viable method for understanding the spatial reciprocity mechanism in nature and hope that it will inspire further studies to resolve social dilemmas.
到目前为止，已有大量研究证明空间拓扑对合作动态（即所谓的“空间互惠”）的促进作用。然而，大多数研究人员可能将其归因于空间布局所支持的策略的正向分类。在本文中，我们分析了不同演化规则下合作演化的时间进程。有趣的是，一个典型的演化过程可分为两个明显的阶段：持久（END）阶段和扩展（EXP）阶段，前者的特征是合作者试图抵御背叛者的入侵，后者则表明完美的C簇快速扩大其区域。我们发现最终的合作水平取决于两个关键因素：END阶段末期完美C簇的形成以及EXP阶段完美C簇的扩展方式。对于确定性规则，C簇边界的平滑扩展使合作者能够达到主导状态，而对于随机规则，粗糙的边界无法为合作的演化提供足够有利的环境。此外，我们表明完美C簇的扩展与相互作用拓扑的聚类系数密切相关。在某种程度上，我们提出了一种可行的方法来理解自然界中的空间互惠机制，并希望它能激发进一步的研究以解决社会困境。
