发表机构
Texas A & M University; University of Colorado, Colorado Springs（德克萨斯农工大学; 科罗拉多大学斯普林斯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究博弈论框架下个体采用logit学习（有限理性）而非模仿学习时，SIS流行病模型中社交距离决策对感染传播的影响，发现低理性可稳定疾病自由均衡，避免不良疫情结局。
AI 中文摘要
我们考虑一个易感-感染-易感（SIS）流行病学模型，其中个体动态地决定是否遵循社交距离。受博弈论收益驱动，他们的行为影响感染的传播。该领域现有的大部分工作考虑的是模仿学习者，导致众所周知的复制者方程。在本文中，我们研究当个体转而采用logit学习规则时，即当个体具有有限理性时，动态结果可能如何发生根本性变化。我们分析了耦合动力系统不同参数区域中存在的均衡的局部渐近稳定性。我们表明，在疾病自由均衡在模仿学习和足够高理性logit学习下不稳定的区域中，足够低的理性可以通过稳定疾病自由均衡来避免这种不良结果。我们还确定了当理性降至阈值以下时，不稳定的地方性均衡得以稳定的参数区域。我们通过数值方法说明了在较低理性程度下，感染状态和响应轨迹收敛到稳定的疾病自由均衡，而随着理性水平上升，相同的轨迹否则收敛到稳定的地方性均衡。我们还比较了复制者动力学下轨迹无法收敛的特定情况，并说明了当理性低于解析推导的阈值时的收敛性。
英文摘要
We consider a susceptible-infected-susceptible (SIS) epidemiological model in which individuals dynamically decide whether to follow social distancing or not. Driven by game-theoretic payoffs, their actions influence the spread of infection. Much of the existing work in this area considers individuals that are imitative learners, leading to the well-studied replicator equation. In this paper, we investigate how the dynamical outcomes may fundamentally shift when individuals are instead equipped with logit learning rules, i.e., when individuals possess bounded rationality. We analyze the local asymptotic stability of equilibria that exist in different parameter regimes of the coupled dynamical system. We show that in regimes where the disease-free equilibrium is unstable under imitative learning and sufficiently high-rationality logit learning, sufficiently low rationality can avoid such an undesirable outcome by stabilizing the disease-free equilibrium. We also identify parameter regimes in which an unstable endemic equilibrium stabilizes when rationality falls below a threshold. We numerically illustrate the convergence of infection state and response trajectories to a stable disease-free equilibrium at a lower degree of rationality, whereas the same trajectories otherwise converge to a stable endemic equilibrium as the rationality level rises. We also compare a specific case in which trajectories under replicator dynamics fail to converge, and illustrate convergence when rationality is below an analytically derived threshold.
