  We study the traffic routing game among a large number of selfish drivers
over a traffic network. We consider a specific scenario where the strategic
drivers can be classified into teams, where drivers in the same team have
identical payoff functions. An incentive mechanism is considered to mitigate
congestion, where each driver is subject to dynamic tax penalties. We explore a
special case in which the tax is affine in the logarithm of the number of
drivers selecting the same route from each team. It is shown via a mean-field
approximation that a Nash equilibrium in the limit of a large population can be
found by linearly solvable algorithms.
