  In this study, we analyse the convergence and stability of dynamic system
optimal (DSO) traffic assignment with fixed departure times. We first formulate
the DSO traffic assignment problem as a strategic game wherein atomic users
select routes that minimise their marginal social costs, called a 'DSO game'.
By utilising the fact that the DSO game is a potential game, we prove that a
globally optimal state is a stochastically stable state under the logit
response dynamics, and the better/best response dynamics converges to a locally
optimal state. Furthermore, as an application of DSO assignment, we examine
characteristics of the evolutionary implementation scheme of marginal cost
pricing. Through theoretical comparison with a fixed pricing scheme, we found
the following properties of the evolutionary implementation scheme: (i) the
total travel time decreases smoother to an efficient traffic state as
congestion externalities are perfectly internalised; (ii) a traffic state would
reach a more efficient state as the globally optimal state is stabilised.
Numerical experiments also suggest that these properties make the evolutionary
scheme robust in the sense that they prevent a traffic state from going to
worse traffic states with high total travel times.
