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.

本研究解决了动态斯塔克尔博格博弈中跟随者最佳响应算子难以解析求解的问题。通过提出一种基于注意力的神经算子，本论文展示了跟随者的最佳响应可以在紧凑的领导者控制集合上进行近似实现，且采用该算子的博弈价值接近于原始博弈。这一结果为解决复杂博弈提供了新的智能方法。

神经算子可以进行动态斯塔克尔博格博弈