  We analyze the behavior of a large number of strategic drivers traveling over
an urban traffic network using the mean-field game framework. We assume an
incentive mechanism for congestion mitigation under which each driver selecting
a particular route is charged a tax penalty that is affine in the logarithm of
the number of agents selecting the same route. We show that the mean-field
approximation of such a large-population dynamic game leads to the so-called
linearly solvable Markov decision process, implying that an open-loop
$\epsilon$-Nash equilibrium of the original game can be found simply by solving
a finite-dimensional linear system.
