Neural Operators Can Play Dynamic Stackelberg Games
Abstract
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.
Keywords
Cite
@article{arxiv.2411.09644,
title = {Neural Operators Can Play Dynamic Stackelberg Games},
author = {Guillermo Alvarez and Ibrahim Ekren and Anastasis Kratsios and Xuwei Yang},
journal= {arXiv preprint arXiv:2411.09644},
year = {2024}
}