  Tolling in traffic networks offers a popular measure to minimize overall
congestion. Existing toll designs primarily focus on congestion in route-based
traffic assignment models (TAMs), in which travelers make a single route
selection from their source to destination. However, these models do not
reflect real-world traveler decisions because they preclude deviations from a
chosen route, and because the enumeration of all routes is computationally
expensive. To address these limitations, our work focuses on arc-based TAMs, in
which travelers sequentially select individual arcs (or edges) on the network
to reach their destination. We first demonstrate that marginal pricing, a
tolling scheme commonly used in route-based TAMs, also achieves socially
optimal congestion levels in our arc-based formulation. Then, we use perturbed
best response dynamics to model the evolution of travelers' arc selection
preferences over time, and a marginal pricing scheme to the social planner's
adaptive toll updates in response. We prove that our adaptive learning and
marginal pricing dynamics converge to a neighborhood of the socially optimal
loads and tolls. We then present empirical results that verify our theoretical
claims.
