The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how, for a population of myopic agents with homogeneous preferences, changes in the environment caused by current aggregate behavior may affect future payoffs and hence alter future behavior. The interaction between the agents is based on a symmetric two-strategy game with positive externalities and negative feedback from aggregate behavior to payoffs, so that at every point in time the population has an incentive to coordinate, whereas over time the more popular strategy becomes less appealing. Under the best response dynamics and the logit dynamics with small noise levels the joint trajectories of preferences and behavior converge to closed orbits around the unique steady state, whereas for large noise levels the steady state of the logit dynamics becomes a sink. Under the replicator dynamics the unique steady state of the system is repelling and the trajectories are unbounded unstable spirals.

这篇论文提出了一个双速演化模型，其中人口博弈（或者，个人偏好）的收益缓慢地适应人口总体行为的变化。该模型研究了对于一群具有同质偏好的近视者，当前总体行为引起的环境变化如何影响未来的收益，从而改变未来的行为。代理之间的交互基于对称的双策略博弈，具有正外部性和从聚合行为到收益的负反馈，因此在每个时间点，人口都有协调的动机，而随着时间的推移，更受欢迎的策略变得越来越少有吸引力。在最佳响应动力学和具有小噪声水平的 logit 动力学下，偏好和行为的联合轨迹收敛到围绕唯一稳态的闭合轨道，而对于大噪声水平，logit 动力学的稳态变为汇。在复制器动力学下，系统的独特稳态是排斥的，轨迹是无限的不稳定螺旋。