Neural Operators Can Play Dynamic Stackelberg Games

ArXiv ID: 2411.09644 “View on arXiv”

Authors: Unknown

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: Dynamic Stackelberg Games, Neural Operators, Attention Mechanisms, Game Theory, Stochastic Processes, N/A (Theoretical)

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper presents highly advanced mathematical analysis involving stochastic processes, universal approximation theorems, and operator theory, but lacks any empirical backtesting, implementation details, or performance metrics, focusing entirely on theoretical guarantees.

  flowchart TD
    A["Research Goal:<br/>Approximate Best-Response in<br/>Dynamic Stackelberg Games"] --> B["Data/Input:<br/>Adapted Open-Loop<br/>Leader Controls"]
    B --> C["Methodology:<br/>Attention-Based Neural Operator"]
    C --> D["Computational Process:<br/>Universal Approximation of<br/>Follower's Best-Response Operator"]
    D --> E{"Outcome / Finding"}
    E --> F["Theorem 1:<br/>Uniform Approximation on<br/>Compact Subsets"]
    E --> G["Theorem 2:<br/>Value Approximation<br/>of Original Game"]