Neural Operators Can Play Dynamic Stackelberg Games
This provides a computational method for solving complex two-player games in economics and AI, though it is incremental as it builds on existing neural operator frameworks.
The paper tackles the intractability of solving dynamic Stackelberg games by approximating the follower's best-response operator with an attention-based neural operator, showing that this approximation uniformly works on compact control subsets and yields game values close to the original.
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.