We consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers selecting the same route. We show that the mean-field approximation of such a game leads to the so-called linearly solvable Markov decision process, implying that its mean-field equilibrium (MFE) can be found simply by solving a finite-dimensional linear system backward in time. Based on this backward-only characterization, it is further shown that the obtained MFE has the notable property of strong time-consistency. A connection between the obtained MFE and a particular class of fictitious play is also discussed.

中文翻译：

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线性可解平均场交通路由博弈


我们考虑涉及大量驾驶员的城市道路网络上的动态交通路由游戏，其中每个选择特定路线的驾驶员都会受到与选择同一路线的驾驶员数量的对数仿射的惩罚。我们证明了这种博弈的平均场近似导致了所谓的线性可解马尔可夫决策过程，这意味着可以通过向后求解有限维线性系统来简单地找到其平均场平衡（MFE）。基于这种仅向后的表征，进一步表明所获得的MFE具有强时间一致性的显着特性。还讨论了获得的 MFE 与特定类别的虚拟游戏之间的联系。