Hierarchical Strategic Decision-Making in Layered Mobility Systems

TL;DR

This paper introduces a hierarchical game-theoretic model combined with feedback optimization to improve decision-making in complex urban mobility systems, demonstrating better outcomes than traditional methods.

Contribution

It presents a novel tri-level Stackelberg game approach with a model-free feedback scheme for scalable, constraint-enforcing policy optimization in mobility systems.

Findings

Our method outperforms Bayesian optimization and genetic algorithms in municipal objectives.

It increases multimodal usage and operator objectives through feedback-based regulation.

The approach achieves tangible welfare gains in a real Zurich mobility network.

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.