AI 中文总结
该研究提出k级可区分机制，通过新型博弈结构评估LLMs的策略深度，发现递归推理下模型策略深度准确，对手博弈的归纳推理会降低性能，明确策略心智化可提升表现。
AI 中文摘要
推理的策略深度是在有限理性环境中运行的大型语言模型（LLMs）人类交互的关键要素。然而，现有评估主要基于预训练语料库中普遍存在的经典博弈，难以区分真正的策略推理与记忆。为解决这一问题，我们为策略深度推理形式化了必要的k级可区分条件，并构建了一套符合该标准的新型博弈结构。利用这些博弈，我们从思维链（Chain-of-Thought）标记和递归推理下的实际行动、对手博弈数据的归纳轨迹两方面评估LLMs的策略深度。在涵盖四个LLMs、四种博弈结构以及十层迭代推理的实验中，我们发现模型在递归推理下能保持准确的策略深度，且在每一层的陈述推理与行动之间具有很强的内部一致性。错误源于使用了错误的迭代推理步骤数，而非计算最优响应时出错。不过，从对手博弈进行的归纳推理会使准确性急剧下降，且在不同博弈间表现不均，而思维链中明确的策略心智化能显著提升整体性能。
英文摘要
Strategic depth of reasoning is essential for human interaction of Large Language Models (LLMs) operating in boundedly rational environments. However, existing evaluations are primarily based on canonical games prevalent in pretraining corpora, making it difficult to disentangle true strategic reasoning from memorisation. To address this, we formalise a necessary level-K distinguishability condition for strategic depth inference and construct a suite of novel game structures that meet this standard. Using these games, we evaluate strategic depth in LLMs from both the Chain-of-Thought tokens and actual actions under recursive reasoning and an inductive trace of opponent game-play data. Across experimental trials spanning four LLMs, four game structures, and ten levels of iterated reasoning, we find that model models maintain accurate strategic depth under recursive reasoning, with strong internal consistency between stated reasoning and actions at every level. Errors arise from using the wrong number of iterated depth of reasoning steps, not from computing best responses incorrectly. However, inductive inference from opponent play degrades accuracy sharply and unevenly across games, and explicit strategic mentalizing in the chain of thought substantially improves overall performance.
