Hierarchical Strategic Decision-Making in Layered Mobility Systems
Mingjia He, Zhiyu He, Jan Ghadamian, Florian Dörfler, Emilio Frazzoli, Gioele Zardini
TL;DR
The paper tackles hierarchical decision-making in multimodal urban mobility by formulating a tri-level Stackelberg game among travelers ($\mathbf{y}$), operators ($\mathbf{x}$), and the municipality ($\mathbf{z}$) and solving it with a model-free feedback optimization loop. Lower-level equilibria are computed (travelers via a Beckmann reformulation solved with Frank-Wolfe, operators via best-responses), while the municipality updates policy using projected two-point gradient estimates, without differentiating through inner mappings. A neural-network surrogate is used offline to approximate the middle-level equilibrium to accelerate online evaluations. On Zurich's real multimodal network, the approach yields substantially better municipal objectives than Bayesian optimization or genetic algorithms and reveals integration incentives that increase multimodal usage and improve operator outcomes, highlighting the potential to steer competition toward cooperative welfare gains in data-rich mobility systems.
Abstract
Mobility systems are complex socio-technical environments influenced by multiple stakeholders with hierarchically interdependent decisions, rendering effective control and policy design inherently challenging. We bridge hierarchical game-theoretic modeling with online feedback optimization by casting urban mobility as a tri-level Stackelberg game (travelers, operators, municipality) closed in a feedback loop. The municipality iteratively updates taxes, subsidies, and operational constraints using a projected two-point (gradient-free) scheme, while lower levels respond through equilibrium computations (Frank-Wolfe for traveler equilibrium; operator best responses). This model-free pipeline enforces constraints, accommodates heterogeneous users and modes, and scales to higher-dimensional policy vectors without differentiating through equilibrium maps. On a real multimodal network for Zurich, Switzerland, our method attains substantially better municipal objectives than Bayesian optimization and Genetic algorithms, and identifies integration incentives that increase multimodal usage while improving both operator objectives. The results show that feedback-based regulation can steer competition toward cooperative outcomes and deliver tangible welfare gains in complex, data-rich mobility ecosystems.