No-Regret Learning in Stackelberg Games with an Application to Electric Ride-Hailing
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918241439318016 |
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| author | Maddux, Anna Maljkovic, Marko Geroliminis, Nikolas Kamgarpour, Maryam |
| author_facet | Maddux, Anna Maljkovic, Marko Geroliminis, Nikolas Kamgarpour, Maryam |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_03745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | No-Regret Learning in Stackelberg Games with an Application to Electric Ride-Hailing Maddux, Anna Maljkovic, Marko Geroliminis, Nikolas Kamgarpour, Maryam Systems and Control Computer Science and Game Theory 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. |
| title | No-Regret Learning in Stackelberg Games with an Application to Electric Ride-Hailing |
| topic | Systems and Control Computer Science and Game Theory |
| url | https://arxiv.org/abs/2504.03745 |