  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.
