A Convex Formulation of Game-theoretic Hierarchical Routing
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913742391869440 |
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| author | Lee, Dong Ho Donnel, Kaitlyn Li, Max Z. Fridovich-Keil, David |
| author_facet | Lee, Dong Ho Donnel, Kaitlyn Li, Max Z. Fridovich-Keil, David |
| contents | Hierarchical decision-making is a natural paradigm for coordinating multi-agent systems in complex environments such as air traffic management. In this paper, we present a bilevel framework for game-theoretic hierarchical routing, where a high-level router assigns discrete routes to multiple vehicles who seek to optimize potentially noncooperative objectives that depend upon the assigned routes. To address computational challenges, we propose a reformulation that preserves the convexity of each agent's feasible set. This convex reformulation enables a solution to be identified efficiently via a customized branch-and-bound algorithm. Our approach ensures global optimality while capturing strategic interactions between agents at the lower level. We demonstrate the solution concept of our framework in two-vehicle and three-vehicle routing scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Convex Formulation of Game-theoretic Hierarchical Routing Lee, Dong Ho Donnel, Kaitlyn Li, Max Z. Fridovich-Keil, David Multiagent Systems Computer Science and Game Theory Hierarchical decision-making is a natural paradigm for coordinating multi-agent systems in complex environments such as air traffic management. In this paper, we present a bilevel framework for game-theoretic hierarchical routing, where a high-level router assigns discrete routes to multiple vehicles who seek to optimize potentially noncooperative objectives that depend upon the assigned routes. To address computational challenges, we propose a reformulation that preserves the convexity of each agent's feasible set. This convex reformulation enables a solution to be identified efficiently via a customized branch-and-bound algorithm. Our approach ensures global optimality while capturing strategic interactions between agents at the lower level. We demonstrate the solution concept of our framework in two-vehicle and three-vehicle routing scenarios. |
| title | A Convex Formulation of Game-theoretic Hierarchical Routing |
| topic | Multiagent Systems Computer Science and Game Theory |
| url | https://arxiv.org/abs/2503.13790 |