Level-k Distinguishable Mechanisms for Evaluating Bounded Rationality in LLMs
2026-08-21 • Multiagent Systems
Multiagent Systems
AI summaryⓘ
The authors studied how well large language models (LLMs) can think several steps ahead strategically, like in a game. They created new games designed specifically to test true strategic thinking, not just memorized answers. Their tests showed that LLMs are generally good at reasoning multiple steps ahead when working through the problem themselves, but they struggle when trying to guess an opponent's moves based on past play. Including explicit thinking steps about the opponent’s strategy helps improve their performance. Mistakes usually come from guessing the wrong number of thinking steps, not from poor decision-making at each step.
Large Language ModelsStrategic DepthLevel-K ReasoningChain-of-ThoughtIterated ReasoningBoundedly Rational EnvironmentsGame TheoryInductive InferenceStrategic Mentalizing
Authors
Binchi Zhang, Atrisha Sarkar
Abstract
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.