  This paper investigates the dynamic stability of an adaptive learning
procedure in a traffic game. Using the Routh-Hurwitz criterion we study the
stability of the rest points of the corresponding mean field dynamics. In the
special case with two routes and two players we provide a full description of
the number and nature of these rest points as well as the global asymptotic
behavior of the dynamics. Depending on the parameters of the model, we find
that there are either one, two or three equilibria and we show that in all
cases the mean field trajectories converge towards a rest point for almost all
initial conditions.
