  We study the distribution of traffic in networks whose users try to minimise
their delays by adhering to a simple learning scheme inspired by the replicator
dynamics of evolutionary game theory. The stable steady states of these
dynamics coincide with the network's Wardrop equilibria and form a convex
polytope whose dimension is determined by the network's redundancy (an
important concept which measures the "linear dependence" of the users' paths).
Despite this abundance of stationary points, the long-term behaviour of the
replicator dynamics turns out to be remarkably simple: every solution orbit
converges to a Wardrop equilibrium.
  On the other hand, a major challenge occurs when the users' delays fluctuate
unpredictably due to random external factors. In that case, interior equilibria
are no longer stationary, but strict equilibria remain stochastically stable
irrespective of the fluctuations' magnitude. In fact, if the network has no
redundancy and the users are patient enough, we show that the long-term
averages of the users' traffic flows converge to the vicinity of an
equilibrium, and we also estimate the corresponding invariant measure.
