For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often become increasingly complicated to interpret. To tackle this problem, we introduce persistent homology as a rigorous framework that can be used to both define and compute higher-order features of data in a manner which is invariant to parameter choices, robust to noise, and independent of human observation. Our work demonstrates its relevance for spatial games by showing how topological features of simulation data that persist over different spatial scales reflect the stability of strategies in 2D lattice games. To do so, we analyze the persistent homology of scenarios from two games: a Prisoner’s Dilemma and a SIRS epidemic model. The experimental results show how the method accurately detects features that correspond to real aspects of the game dynamics. Unlike other tools that study dynamics of spatial systems, persistent homology can tell us something meaningful about population structure while remaining neutral about the underlying structure itself. Regardless of game complexity, since strategies either succeed or fail to conform to shapes of a certain topology there is much potential for the method to provide novel insights for a wide variety of spatially extended systems in biology, social science, and physics.

近三十年来，空间博弈为研究行为及其与人口结构的关系提供了丰富的见解。然而，随着不同规则和因素的添加或改变，空间模型的动态往往变得越来越难以解释。为了解决这个问题，我们引入了持久同源性作为一个严格的框架，该框架可用于以对参数选择不变、对噪声具有鲁棒性并且独立于人类观察的方式来定义和计算数据的高阶特征。我们的工作通过展示在不同空间尺度上持续存在的模拟数据的拓扑特征如何反映 2D 格子游戏中策略的稳定性，证明了其与空间游戏的相关性。为此，我们分析了两个游戏场景的持久同源性：囚徒困境和 SIRS 流行病模型。实验结果显示了该方法如何准确地检测与游戏动态的真实方面相对应的特征。与研究空间系统动力学的其他工具不同，持久同源性可以告诉我们一些关于种群结构的有意义的信息，同时对底层结构本身保持中立。不管游戏的复杂性如何，由于策略要么成功要么不符合某种拓扑的形状，该方法就有很大的潜力为生物学、社会科学和物理学中的各种空间扩展系统提供新的见解。持久的同源性可以告诉我们关于种群结构的一些有意义的信息，同时对底层结构本身保持中立。不管游戏的复杂性如何，由于策略要么成功要么不符合某种拓扑的形状，该方法就有很大的潜力为生物学、社会科学和物理学中的各种空间扩展系统提供新的见解。持久的同源性可以告诉我们关于种群结构的一些有意义的信息，同时对底层结构本身保持中立。不管游戏的复杂性如何，由于策略要么成功要么不符合某种拓扑的形状，该方法就有很大的潜力为生物学、社会科学和物理学中的各种空间扩展系统提供新的见解。