Year: 2024
Type: article
Abstract: We consider the problem of efficiently learning to play single-leader multi-follower Stackelberg games when the leader lacks knowledge of the lower-level game. Such games arise in hierarchical decision-making problems involving self-interested agents. For example, in electric ride-hailing markets, a central authority aims to learn optimal charging prices to shape fleet distributions and charging patterns of ride-hailing companies. Existing works typically apply gradient-based methods to find the leader's optimal strategy. Such methods are impractical as they require that the followers share private utility information with the leader. Instead, we treat the lower-level game as a black box, assuming only that the followers' interactions approximate a Nash equilibrium while the leader observes the realized cost of the resulting approximation. Under kernel-based regularity assumptions on the leader's cost function, we develop a no-regret algorithm that converges to an $ε$-Stackelberg equilibrium in $O(\sqrt{T})$ rounds. Finally, we validate our approach through a numerical case study on optimal pricing in electric ride-hailing markets.
Source: IEEE Control Systems
Authors: Maddux, Anna, Maljkovic, Marko, Geroliminis, Nikolas, Kamgarpour, Maryam
Language: English
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4404316905