Gómez-Gardeñes J, Campillo M, Floría L M, Moreno Y
Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain.
Phys Rev Lett. 2007 Mar 9;98(10):108103. doi: 10.1103/PhysRevLett.98.108103. Epub 2007 Mar 7.
In this Letter, we study how cooperation is organized in complex topologies by analyzing the evolutionary (replicator) dynamics of the prisoner's dilemma, a two-player game with two available strategies, defection and cooperation, whose payoff matrix favors defection. We show that, asymptotically, the population is partitioned into three subsets: individuals that always cooperate (pure cooperators), always defect (pure defectors), and those that intermittently change their strategy. In fact, the size of the later set is the biggest for a wide range of the "stimulus to defect" parameter. While in homogeneous random graphs pure cooperators are grouped into several clusters, in heterogeneous scale-free (SF) networks they always form a single cluster containing the most connected individuals (hubs). Our results give further insights into why cooperation in SF networks is enhanced.
在本信函中，我们通过分析囚徒困境的进化（复制者）动力学来研究复杂拓扑结构中合作是如何组织的。囚徒困境是一种双人博弈，有背叛和合作两种可用策略，其收益矩阵有利于背叛。我们表明，渐近地，种群被划分为三个子集：总是合作的个体（纯合作者）、总是背叛的个体（纯背叛者）以及那些间歇性改变策略的个体。事实上，对于广泛的“背叛刺激”参数范围，后一组的规模是最大的。在均匀随机图中，纯合作者被分组到几个簇中，而在异质无标度（SF）网络中，它们总是形成一个包含连接性最强个体（中心节点）的单一簇。我们的结果进一步深入探讨了为什么SF网络中的合作会得到增强。
