Neural Operators Can Play Dynamic Stackelberg Games
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915020512690176 |
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| author | Alvarez, Guillermo Ekren, Ibrahim Kratsios, Anastasis Yang, Xuwei |
| author_facet | Alvarez, Guillermo Ekren, Ibrahim Kratsios, Anastasis Yang, Xuwei |
| contents | Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately, only stylized Stackelberg games are explicitly solvable since the follower's best-response operator (as a function of the control of the leader) is typically analytically intractable. This paper addresses this issue by showing that the \textit{follower's best-response operator} can be approximately implemented by an \textit{attention-based neural operator}, uniformly on compact subsets of adapted open-loop controls for the leader. We further show that the value of the Stackelberg game where the follower uses the approximate best-response operator approximates the value of the original Stackelberg game. Our main result is obtained using our universal approximation theorem for attention-based neural operators between spaces of square-integrable adapted stochastic processes, as well as stability results for a general class of Stackelberg games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neural Operators Can Play Dynamic Stackelberg Games Alvarez, Guillermo Ekren, Ibrahim Kratsios, Anastasis Yang, Xuwei Optimization and Control Machine Learning Numerical Analysis Probability Computational Finance Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately, only stylized Stackelberg games are explicitly solvable since the follower's best-response operator (as a function of the control of the leader) is typically analytically intractable. This paper addresses this issue by showing that the \textit{follower's best-response operator} can be approximately implemented by an \textit{attention-based neural operator}, uniformly on compact subsets of adapted open-loop controls for the leader. We further show that the value of the Stackelberg game where the follower uses the approximate best-response operator approximates the value of the original Stackelberg game. Our main result is obtained using our universal approximation theorem for attention-based neural operators between spaces of square-integrable adapted stochastic processes, as well as stability results for a general class of Stackelberg games. |
| title | Neural Operators Can Play Dynamic Stackelberg Games |
| topic | Optimization and Control Machine Learning Numerical Analysis Probability Computational Finance |
| url | https://arxiv.org/abs/2411.09644 |