标题： 双极化在动态有向图上的稳定性：一种涌现博弈的视角 显示英文标题

标题： The stability of bi-polarization on dynamical directed graphs: an emergent game perspective

摘要： 本文提出了一种有向图和三种观点的共同进化模型，即保守$(+)$、中立$(\odot)$和自由$(-)$。 代理人在更新观点和社会关系时带有偏见。 我们发现，在罕见观点更新极限和大系统规模极限下，一种涌现博弈足以预测双极化的稳定性。 只有当涌现博弈具有内部纳什均衡时，双极化才是稳定的。 必要且充分条件通过风险优势和进化稳定性来解释。 这种博弈方法使我们能够揭示实证系统中双极化的稳定性。 我们的工作促进了对争议性话题观点形成的理解，并展示了观点动态与进化博弈论之间的深刻联系。 显示英文摘要

摘要： This paper proposes a co-evolutionary model of directed graphs and three opinions, i.e., conservative$(+)$, neutral$(\odot)$ and liberal$(-)$. Agents update both opinions and social relationships with bias. We find that an emergent game suffices to predict the stability of bi-polarization under a rare opinion updating limit and a large system size limit. The bi-polarization is stable if and only if the emergent game has an internal Nash equilibrium. The necessary and sufficient condition is explained by both risk dominance and evolutionary stability. This game approach facilitates us to reveal the stability of bi-polarization in empirical systems. Our work fosters the understanding of opinion formation for controversial topics, and shows a deep connection between opinion dynamics and evolutionary game theory.