  In this paper, we consider a large class of hierarchical congestion
population games. One can show that the equilibrium in a game of such type can
be described as a minimum point in a properly constructed multi-level convex
optimization problem. We propose a fast primal-dual composite gradient method
and apply it to the problem, which is dual to the problem describing the
equilibrium in the considered class of games. We prove that this method allows
to find an approximate solution of the initial problem without increasing the
complexity.
