  Congestion games are a classical type of games studied in game theory, in
which n players choose a resource, and their individual cost increases with the
number of other players choosing the same resource. In network congestion games
(NCGs), the resources correspond to simple paths in a graph, e.g. representing
routing options from a source to a target. In this paper, we introduce a
variant of NCGs, referred to as dynamic NCGs: in this setting, players take
transitions synchronously, they select their next transitions dynamically, and
they are charged a cost that depends on the number of players simultaneously
using the same transition.
  We study, from a complexity perspective, standard concepts of game theory in
dynamic NCGs: social optima, Nash equilibria, and subgame perfect equilibria.
Our contributions are the following: the existence of a strategy profile with
social cost bounded by a constant is in PSPACE and NP-hard. (Pure) Nash
equilibria always exist in dynamic NCGs; the existence of a Nash equilibrium
with bounded cost can be decided in EXPSPACE, and computing a witnessing
strategy profile can be done in doubly-exponential time. The existence of a
subgame perfect equilibrium with bounded cost can be decided in 2EXPSPACE, and
a witnessing strategy profile can be computed in triply-exponential time.
