Neural Operators Can Play Dynamic Stackelberg Games

TL;DR

This paper introduces a neural operator approach to approximate the follower's best-response in dynamic Stackelberg games, enabling solutions for more complex, intractable game scenarios.

Contribution

It develops a universal approximation theorem for attention-based neural operators to model the follower's best-response in Stackelberg games.

Findings

Neural operators can approximate the follower's best-response operator.

The approximate Stackelberg game value converges to the original game value.

The method applies to a broad class of stochastic 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.