Equilibrium and regularity issues for congested dynamics

Abstract

In this seminar, we present a model for optimal transport with congestion effects: we will address both the discrete and the continuous case. From an individual viewpoint, we can introduce in a natural way a kind of Nash equilibrium, which in this context is usually called Wardrop equilibrium. Then existence of these equilibria can be shown by minimizing a suitable total transportation cost. More important, in the continuous case, when the coupling between the sources and the destinations is not fixed and the data are sufficiently “well behaved”, we can characterize these equilibria in terms of a flow, driven by a vector field parallel to the gradient of an optimal price. Part of the results here presented are contained