Nash Flows Over Time with Tolls
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911211856068608 |
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| author | Rosner, Shaul Schröder, Marc Koch, Laura Vargas |
| author_facet | Rosner, Shaul Schröder, Marc Koch, Laura Vargas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nash Flows Over Time with Tolls Rosner, Shaul Schröder, Marc Koch, Laura Vargas Computer Science and Game Theory Optimization and Control 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. |
| title | Nash Flows Over Time with Tolls |
| topic | Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2510.13518 |