用不确定性引导推理，让大模型下棋更聪明。
LLMs for Game Theory: Entropy-Guided In-Context Learning and Adaptive CoT Reasoning
- 根据推理不确定度动态调整思考路径和示例数量
- 游戏胜率从-11.6%提升至+9.5%，且调用次数少
- 适合需要精准决策的博弈类任务研究者
我们提出一种基于大模型的离散博弈推理框架，以井字棋为例。该方法结合上下文学习与熵引导的思维链（CoT）推理，实现自适应上下文检索。模型根据分词级不确定性动态调整：低不确定性时采用简洁推理与最少上下文，高不确定性则触发多路径扩展式推理。实验对比次优算法对手，在100局游戏中，熵感知自适应推理使平均对局结果从基准模型的-11.6%提升至+9.5%（胜=+1，平=0，负=-1），同时保持较低的每局大模型调用次数。统计验证表明提升显著，相关性分析显示分词级熵与走子最优性呈负相关。结果证明，基于不确定性的自适应推理能有效提升大模型在序列决策环境中的表现。
原文摘要 · Abstract (English)
We propose a novel LLM-based framework for reasoning in discrete, game-theoretic tasks, illustrated with \emph{Tic-Tac-Toe}. The method integrates in-context learning with entropy-guided chain-of-thought (CoT) reasoning and adaptive context retrieval. The model dynamically adjusts both the number of retrieved examples and reasoning paths according to token-level uncertainty: concise reasoning with minimal context is used when uncertainty is low, whereas higher uncertainty triggers expanded multi-path CoT exploration. Experimental evaluation against a sub-optimal algorithmic opponent shows that entropy-aware adaptive reasoning substantially improves decision quality, increasing the average game outcome from \(-11.6\%\) with the baseline LLM to \(+9.5\%\) with entropy-guided adaptive reasoning over 100 games (win = +1, tie = 0, loss = -1), while maintaining a relatively low number of LLM queries per game. Statistical validation confirms that the improvement is significant, and correlation analysis reveals a negative association between token-level entropy and move optimality. These findings demonstrate that uncertainty-guided adaptive reasoning effectively enhances LLM performance in sequential decision-making environments.
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