Qian Xiaolan, Xu Fangqian, Yang Junzhong, Kurths Jürgen
School of Electronics and Information, Zhejiang University of Media and Communications, Hangzhou 310018, China.
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Chaos. 2015 Apr;25(4):043115. doi: 10.1063/1.4919080.
The prisoner's dilemma (PD), in which players can either cooperate or defect, is considered a paradigm for studying the evolution of cooperation in spatially structured populations. There the compact cooperator cluster is identified as a characteristic pattern and the probability of forming such pattern in turn depends on the features of the networks. In this paper, we investigate the influence of expansion of neighborhood on pattern formation by taking a weak PD game with one free parameter T, the temptation to defect. Two different expansion methods of neighborhood are considered. One is based on a square lattice and expanses along four directions generating networks with degree increasing with K=4m. The other is based on a lattice with Moore neighborhood and expanses along eight directions, generating networks with degree of K=8m. Individuals are placed on the nodes of the networks, interact with their neighbors and learn from the better one. We find that cooperator can survive for a broad degree 4≤K≤70 by taking a loose type of cooperator clusters. The former simple corresponding relationship between macroscopic patterns and the microscopic PD interactions is broken. Under a condition that is unfavorable for cooperators such as large T and K, systems prefer to evolve to a loose type of cooperator clusters to support cooperation. However, compared to the well-known compact pattern, it is a suboptimal strategy because it cannot help cooperators dominating the population and always corresponding to a low cooperation level.
囚徒困境（PD）中，参与者可以选择合作或背叛，它被视为研究空间结构化群体中合作演化的范例。在这种情况下，紧密的合作者集群被视为一种特征模式，而形成这种模式的概率又取决于网络的特征。在本文中，我们通过采用一个带有自由参数T（背叛诱惑）的弱PD博弈，研究邻域扩展对模式形成的影响。我们考虑了两种不同的邻域扩展方法。一种基于正方形晶格，沿四个方向扩展，生成度随K = 4m增加的网络。另一种基于具有摩尔邻域的晶格，沿八个方向扩展，生成度为K = 8m的网络。个体放置在网络节点上，与邻居相互作用并向更好的邻居学习。我们发现，通过采用一种松散类型的合作者集群，合作者在4≤K≤70的广泛度范围内能够存活。宏观模式与微观PD相互作用之间以前简单的对应关系被打破。在诸如T和K较大等不利于合作者的条件下，系统倾向于演化到一种松散类型的合作者集群以支持合作。然而，与众所周知的紧密模式相比，这是一种次优策略，因为它无法帮助合作者主导群体，并且总是对应于较低的合作水平。
