This paper investigates the rationality of large language models (LLMs) in strategic decision-making contexts, specifically within the framework of game theory. We evaluate several state-of-the-art LLMs across a spectrum of complete-information and incomplete-information games. Our findings reveal that LLMs frequently deviate from rational strategies, particularly as the complexity of the game increases with larger payoff matrices or deeper sequential trees. To address these limitations, we design multiple game-theoretic workflows that guide the reasoning and decision-making processes of LLMs. These workflows aim to enhance the models' ability to compute Nash Equilibria and make rational choices, even under conditions of uncertainty and incomplete information. Experimental results demonstrate that the adoption of these workflows significantly improves the rationality and robustness of LLMs in game-theoretic tasks. Specifically, with the workflow, LLMs exhibit marked improvements in identifying optimal strategies, achieving near-optimal allocations in negotiation scenarios, and reducing susceptibility to exploitation during negotiations. Furthermore, we explore the meta-strategic considerations of whether it is rational for agents to adopt such workflows, recognizing that the decision to use or forgo the workflow constitutes a game-theoretic issue in itself. Our research contributes to a deeper understanding of LLMs' decision-making capabilities in strategic contexts and provides insights into enhancing their rationality through structured workflows. The findings have implications for the development of more robust and strategically sound AI agents capable of navigating complex interactive environments. Code and data supporting this study are available at \url{https://github.com/Wenyueh/game_theory}.

翻译：本文研究大型语言模型（LLM）在战略决策情境中的理性表现，特别是在博弈论框架下的行为。我们评估了多种先进LLM在一系列完全信息与不完全信息博弈中的表现。研究发现，LLM经常偏离理性策略，尤其当博弈复杂度随收益矩阵规模扩大或序列树深度增加而提升时。为应对这些局限，我们设计了多种博弈论工作流，用以引导LLM的推理与决策过程。这些工作流旨在增强模型计算纳什均衡及做出理性选择的能力，即使在不确定性与信息不完全的条件下。实验结果表明，采用这些工作流能显著提升LLM在博弈论任务中的理性与鲁棒性。具体而言，在工作流辅助下，LLM在识别最优策略、在谈判场景中实现接近最优的资源分配、以及降低谈判过程中被利用的脆弱性等方面均表现出显著改进。此外，我们探讨了智能体是否应采用此类工作流的元战略考量——认识到使用或放弃工作流本身即构成一个博弈论问题。本研究有助于深化对LLM在战略情境中决策能力的理解，并为通过结构化工作流提升其理性提供了见解。相关发现对开发更具鲁棒性、战略合理的AI智能体以应对复杂交互环境具有启示意义。支持本研究的代码与数据公开于\url{https://github.com/Wenyueh/game_theory}。