{"ID":2855200,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.13518","arxiv_id":"2510.13518","title":"Nash Flows Over Time with Tolls","abstract":"We study a dynamic routing game motivated by traffic flows. The base model for an edge is the Vickrey bottleneck model. That is, edges are equipped with a free flow transit time and a capacity. When the inflow into an edge exceeds its capacity, a queue forms and the following particles experience a waiting time. In this paper, we enhance the model by introducing tolls, i.e., a cost each flow particle must pay for traversing an edge. In this setting we consider non-atomic equilibria, which means flows over time in which every particle is on a cheapest path, when summing up toll and travel time. We first show that unlike in the non-tolled version of this model, dynamic equilibria are not unique in terms of costs and do not necessarily reach a steady state. As a main result, we provide a procedure to compute steady states in the model with tolls.","short_abstract":"We study a dynamic routing game motivated by traffic flows. The base model for an edge is the Vickrey bottleneck model. That is, edges are equipped with a free flow transit time and a capacity. When the inflow into an edge exceeds its capacity, a queue forms and the following particles experience a waiting time. In thi...","url_abs":"https://arxiv.org/abs/2510.13518","url_pdf":"https://arxiv.org/pdf/2510.13518v1","authors":"[\"Shaul Rosner\",\"Marc Schröder\",\"Laura Vargas Koch\"]","published":"2025-10-15T13:10:03Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"math.OC\"]","methods":"[]","has_code":false}