Locodi A M, O'Riordan C
National University of Ireland Galway, Computer Science, Galway, Ireland.
R Soc Open Sci. 2021 May 5;8(5):201958. doi: 10.1098/rsos.201958.
Identifying the conditions that support cooperation in spatial evolutionary game theory has been the focus of a large body of work. In this paper, the classical Prisoner's Dilemma is adopted as an interaction model; agents are placed on graphs and their interactions are constrained by a graph topology. A simple strategy update mechanism is used where agents copy the best performing strategy of their neighbourhood (including themselves). In this paper, we begin with a fully cooperative population and explore the robustness of the population to the introduction of defectors. We introduce a graph structure that has the property that the initial fully cooperative population is robust to any one perturbation (a change of any cooperator to a defector). We present a proof of this property and specify the necessary constraints on the graph. Furthermore, given the standard game payoffs, we calculate the smallest graph which possesses this property. We present an approach for increasing the size of the graph and we show empirically that this extended graph is robust to an increasing percentage of perturbations. We define a new class of graphs for the purpose of future work.
在空间进化博弈论中，确定支持合作的条件一直是大量研究工作的重点。本文采用经典的囚徒困境作为交互模型；主体被放置在图上，其交互受图拓扑结构的约束。使用一种简单的策略更新机制，即主体复制其邻域（包括自身）中表现最佳的策略。在本文中，我们从一个完全合作的群体开始，探讨该群体对引入背叛者的鲁棒性。我们引入一种图结构，其特性是初始的完全合作群体对任何一个扰动（任何一个合作者变为背叛者的变化）具有鲁棒性。我们给出了这一特性的证明，并指定了图上的必要约束条件。此外，给定标准博弈收益，我们计算出具有此特性的最小图。我们提出一种增加图规模的方法，并通过实验表明这种扩展后的图对不断增加比例的扰动具有鲁棒性。为了未来的工作，我们定义了一类新的图。
