  An universal primal-dual approach of description equilibriums in large class
of hierarchical congestion population games is proposed. At the very core of
the approach is hierarchy of enclosed to each other transport networks. In
different time-scales corresponding logit dynamics on this networks is
considered. This dynamics reflect restricted rationality of the agents.
Searching of equilibrium configuration to the multi-level convex optimization
problem is reduced (in other words variational principle for these class of the
games/models is formulated). Then the dual problem is formulated. This problem
has natural interpretation in turn and it is more computationally attractive
then the primal one. So an effective primal-dual method for this problem is
proposed. This method is based on the composite fast gradient method. Due to
primal-duality the solution of the primal problem from the dual iterative
process is recovered. To fulfil one iteration of this method the rather complex
problem of calculation characteristic function on graph is solved. A special
technique (smooth version of Bellman--Ford approach to the shortest path
problem) is proposed (based on some ideas of Yu. Nesterov) that allows to do it
in a cheap manner. It also should be mentioned that different tricks of small
parameters methods are actively used.
