1 Program for Evolutionary Dynamics, Harvard University , Cambridge, MA , USA.
2 Institute for Quantitative Social Sciences, Harvard University , Cambridge, MA , USA.
J R Soc Interface. 2019 Mar 29;16(152):20180677. doi: 10.1098/rsif.2018.0677.
Cooperation is a major factor in the evolution of human societies. The structure of social networks, which affects the dynamics of cooperation and other interpersonal phenomena, have common structural signatures. One of these signatures is the tendency to organize as groups. This tendency gives rise to networks with community structure, which are composed of distinct modules. In this paper, we study analytically the evolutionary game dynamics on large modular networks in the limit of weak selection. We obtain novel analytical conditions such that natural selection favours cooperation over defection. We calculate the transition point for each community to favour cooperation. We find that a critical inter-community link creation probability exists for given group density, such that the overall network supports cooperation even if individual communities inhibit it. As a byproduct, we present solutions for the critical benefit-to-cost ratio which perform with remarkable accuracy for diverse generative network models, including those with community structure and heavy-tailed degree distributions. We also demonstrate the generalizability of the results to arbitrary two-player games.
合作是人类社会进化的主要因素。影响合作和其他人际现象动态的社会网络结构具有共同的结构特征。这些特征之一是倾向于分组。这种趋势导致具有社区结构的网络，这些网络由不同的模块组成。在本文中，我们在弱选择的极限下对大型模块化网络上的进化博弈动态进行了分析。我们获得了新颖的分析条件，使得自然选择有利于合作而不是背叛。我们计算了每个社区有利于合作的转变点。我们发现，对于给定的群体密度，存在一个临界的社区间链接创建概率，使得整个网络即使个别社区抑制它，也支持合作。作为副产品，我们提出了临界收益-成本比的解决方案，这些解决方案对于不同的生成网络模型，包括具有社区结构和长尾度分布的模型，都具有非常准确的性能。我们还证明了这些结果对任意两人游戏的通用性。
