We study the logit evolutionary dynamics in population games. For general population games, we prove that, on the one hand strict Nash equilibria are locally asymptotically stable under the logit dynamics in the low noise regime, on the other hand a globally exponentially stable fixed point exists in the high noise regime. This suggests the emergence of bifurcations in population games admitting multiple strict Nash equilibria, as verified numerically in previous publications. We then prove sufficient conditions on the game structure for global asymptotic stability of the logit dynamics in every noise regime. Our results find application in particular to heterogeneous routing games, a class of non-potential population games modelling strategic decision-making of users having heterogeneous preferences in transportation networks. In this setting, preference heterogeneities are due, e.g., to access to different sources of information or to different trade-offs between time and money. We show that if the transportation network has parallel routes, then the unique equilibrium of the game is globally asymptotically stable.

翻译：本文研究种群博弈中的Logit演化动力学。对于一般种群博弈，我们证明：一方面，在低噪声条件下，严格纳什均衡在Logit动力学下是局部渐近稳定的；另一方面，在高噪声条件下存在全局指数稳定的不动点。这表明在具有多个严格纳什均衡的种群博弈中可能出现分岔现象，这一点已被先前文献的数值验证所证实。随后，我们证明了在任意噪声条件下Logit动力学全局渐近稳定的博弈结构充分条件。我们的研究结果特别适用于异质路由博弈——一类非势种群博弈，用于建模交通网络中具有异质偏好的用户策略性决策行为。在此设定中，偏好异质性源于用户获取不同信息来源或对时间与金钱的不同折衷。我们证明：若交通网络具有平行路径，则该博弈的唯一均衡是全局渐近稳定的。