SAGE: Structured Strategic Reasoning for Efficient LLM Game Playing

2026-09-28

AI Summary

This study addresses the challenges of unsupported assumptions, inconsistent opponent modeling, and historical interference in large language model-based game-theoretic reasoning. We propose a training-free "Anchor-Adapt-Reconstruct" structured strategic reasoning framework that anchors inference with equilibrium strategies as priors, dynamically adapts to opponent tendencies via soft belief modeling, and eliminates historical noise through counterfactual experience distillation. This approach synergistically integrates uncertainty-aware lookahead and opponent modeling into the reasoning pipeline. Experimental results demonstrate that the proposed framework increases expected returns by 127.6% and reduces token consumption by over 80% in Liar's Dice, while consistently maintaining non-negative expected payoffs across diverse game settings.

Abstract

A strong LLM strategic agent should reason prospectively over uncertain futures, adapt its strategy to opponents' behavioral tendencies, and continuously recalibrate its decision process from interaction experience. However, incorporating these sources in free-form reasoning could lead to unsupported strategic assumptions, inconsistent opponent estimates, and harmful interference from irrelevant historical interactions. To address these issues, we propose SAGE, a training-free inference-time framework that structures LLM strategic reasoning around three coordinated operations: anchor, adapt, and recalibrate. SAGE first anchors reasoning to an equilibrium policy that provides a strategically valid prior. It then conditions deviations from this anchor on a soft belief over opponent behavioral tendencies, enabling opponent-specific exploitation. Finally, SAGE distills strategically related interactions into counterfactual hypotheses about previously missing considerations, allowing past experience to recalibrate the model's reasoning. We evaluate SAGE on three repeated imperfect-information games: Leduc Hold'em, Liar's Dice, and Goofspiel, against various opponent types in each game. Compared with reasoning-intensive LLM agents, including Suspicion-Agent, ReTA, Agent-Pro, EMO, and Hypothetical Minds, SAGE achieves up to a 127.6% payoff improvement in Liar's Dice while reducing input and output token usage by up to 80% and 90%, respectively. In direct match-up play, it attains non-negative mean payoff against 5/10, 8/10, and 8/10 evaluated opponents in Leduc Hold'em, Liar's Dice, and Goofspiel, respectively, while using relatively fewer tokens. Code is available at https://github.com/chenzhwsysu57/SAGE.

Problem

• Large Language Models
• Strategic Reasoning
• Imperfect-Information Games
• Opponent Modeling
• Game Playing

Innovation

• Structured Strategic Reasoning
• Training-free Framework
• Imperfect-information Games
• Equilibrium Policy
• Counterfactual Hypotheses