A Convex Formulation of Game-theoretic Hierarchical Routing

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.

@article{lee2025_2503.13790,
  title={ A Convex Formulation of Game-theoretic Hierarchical Routing },
  author={ Dong Ho Lee and Kaitlyn Donnel and Max Z. Li and David Fridovich-Keil },
  journal={arXiv preprint arXiv:2503.13790},
  year={ 2025 }
}