Game of Thought: Robust Information Seeking with Large Language Models Using Game Theory

TL;DR

This paper introduces a game-theoretic framework called Game of Thought to improve the information-seeking capabilities of large language models, especially in worst-case scenarios, by formalizing the problem as a strategic game and approximating Nash equilibrium strategies.

Contribution

It formalizes the Strategic Language Search problem as a two-player game and proposes a novel game-theoretic approach to enhance LLMs' worst-case information-seeking performance.

Findings

Our approach outperforms prompting-based methods in worst-case scenarios.

Game of Thought improves robustness across various settings.

The framework effectively approximates Nash equilibrium strategies.

Abstract

Large Language Models (LLMs) are increasingly deployed in real-world scenarios where they may lack sufficient information to complete a given task. In such settings, the ability to actively seek out missing information becomes a critical capability. Existing approaches to enhancing this ability often rely on simplifying assumptions that degrade \textit{worst-case} performance. This is an issue with serious implications in high-stakes applications. In this work, we use the game of Twenty Questions to evaluate the information-seeking ability of LLMs. We introduce and formalize its adversarial counterpart, the Strategic Language Search (SLS) problem along with its variants as a two-player zero-sum extensive form game. We propose Game of Thought (GoT), a framework that applies game-theoretic techniques to approximate a Nash equilibrium (NE) strategy for the restricted variant of the game. Empirical results demonstrate that our approach consistently improves worst-case performance compared to (1) direct prompting-based methods and (2) heuristic-guided search methods across all tested settings.