Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| author | Bar-Gera, Hillel Boyles, Stephen D. Ravner, Liron |
| author_facet | Bar-Gera, Hillel Boyles, Stephen D. Ravner, Liron |
| contents | Vickrey's classic single-bottleneck departure time choice equilibrium model exhibits instability under many plausible day-to-day learning dynamics. Such instability is not observed in reality -- does this difference stem from the day-to-day dynamics or from one of the simplifying assumptions of the basic model? This paper explores a variant of the basic model with a continuous distribution of schedule delay parameters which we intuitively expect to have more favorable stability properties. To attain tractability we assume a monotonic relationship between earliness and lateness parameters. We first verify the existence and uniqueness of the equilibrium solution for this model. We then study a broad class of day-to-day dynamics satisfying local pressure and order preservation conditions. Our main contribution is a formal proof that, surprisingly, all such day-to-day dynamics in this context are unstable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13831 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability Bar-Gera, Hillel Boyles, Stephen D. Ravner, Liron Computer Science and Game Theory Vickrey's classic single-bottleneck departure time choice equilibrium model exhibits instability under many plausible day-to-day learning dynamics. Such instability is not observed in reality -- does this difference stem from the day-to-day dynamics or from one of the simplifying assumptions of the basic model? This paper explores a variant of the basic model with a continuous distribution of schedule delay parameters which we intuitively expect to have more favorable stability properties. To attain tractability we assume a monotonic relationship between earliness and lateness parameters. We first verify the existence and uniqueness of the equilibrium solution for this model. We then study a broad class of day-to-day dynamics satisfying local pressure and order preservation conditions. Our main contribution is a formal proof that, surprisingly, all such day-to-day dynamics in this context are unstable. |
| title | Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2604.13831 |