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

TL;DR

This paper addresses the challenge of information seeking by large language models under partial observability and worst-case adversarial conditions. It introduces Game of Thought (GoT), a framework that uses depth-limited subgame search and extensive-form game solving to approximate Nash equilibria in Strategic Language Search (SLS) problems, particularly SLSR and WSLS variants, without relying on strong priors about item distributions. By modeling information gathering as a zero-sum extensive-form game and leveraging CFR-based solvers, GoT demonstrates consistent worst-case improvements over direct prompting and Uncertainty of Thought across multiple domains (20Q, medical diagnosis, and troubleshooting), while maintaining competitive average performance. The work also discusses theoretical aspects (even-split NE properties, safe subgame resolving) and practical considerations (question generation via LLMs, caching, and computational trade-offs), highlighting GoT’s potential for robust, high-stakes information gathering in real-world settings.

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.

Figures (10)

• Figure 1: EFG representation of Example \ref{['ex:circular']}. The root node belongs to the Item Chooser and the other nodes belong to the Questioner. Edges in black correspond to the choice of item $s^*$. Colored edges in red, blue, and green refer to questions $q^{(1)}$, $q^{(2)}$, and $q^{(3)}$ respectively. Vertices connected by dotted lines belong to the same infoset. Payoffs (resp. costs) to the Item Chooser (resp. Questioner) are shown in the leaves. We omit edges (and their descendants) where the same question is asked more than once; these are never optimal and correspond to dominated actions.
• Figure 2: An overview of GoT. To choose the question at time step $t$, we (1) perform depth limited simulation (2) Construct a subgame (3) Solve it for a local strategy which (4) informs the choice of the question. Steps 1 to 3 devise the strategy, while step 4 plays the game.
• Figure 3: Worst-case performance of various methods in Weighted Variant on Common and Breeds. The x-axis is $d$, the y-axis is the payoff for the Item Chooser $w_i \cdot|H|$.
• Figure 4: Performance in the weighted variant with artificially skewed weights on Breeds. Graph on the left shows the performance when the additional question is included.
• Figure 5: Average and Worst-Case Performance on DX. The model used is Qwen 2.5 72B Instruct, with $k$ set to 1. Note that the variance in the average performance is due to different samples of $P^o$, not the randomness in the methods themselves.

Theorems & Definitions (14)

• Example 1
• Theorem 3.6
• Theorem 3.7
• Example 2
• Example 3
• Remark 3.9
• Theorem 5.1
• Lemma 2.1
• proof
• Lemma 2.2