Evaluating Counterfactual Strategic Reasoning in Large Language Models

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.

Large language models (LLMs) are increasingly tasked with strategic decision-making under incomplete information, such as in negotiation and policymaking. While LLMs can excel at many such tasks, they also fail in ways that are poorly understood. We shed light on these failures by uncovering two fundamental gaps in the internal mechanisms underlying the decision-making of LLMs in incomplete-information games, supported by experiments with open-weight models Llama 3.1, Qwen3, and gpt-oss. First, an observation-belief gap: LLMs encode internal beliefs about latent game states that are substantially more accurate than their own verbal reports, yet these beliefs are brittle. In particular, the belief accuracy degrades with multi-hop reasoning, exhibits primacy and recency biases, and drifts away from Bayesian coherence over extended interactions. Second, a belief-action gap: The implicit conversion of internal beliefs into actions is weaker than that of the beliefs externalized in the prompt, yet neither belief-conditioning consistently achieves higher game payoffs. These results show how analyzing LLMs' internal processes can expose systematic vulnerabilities that warrant caution before deploying LLMs in strategic domains without robust guardrails.

We introduce a multi-turn interactive framework for reasoning evaluation that treats reasoning as active evidence acquisition and belief updating. Wherein, LLMs receive only the task rules, must issue targeted queries to a hidden environment, integrate partial observations over time, and decide when to submit a final answer. Beyond standard success rate and interaction efficiency, we evaluate contextual robustness under controlled contextual perturbations, and metacognitive adaptation through counterfactual revision and necessity judgment. We instantiate the framework as a benchmark of 474 executable games, each evaluated under five fixed configuration search spaces corresponding to five difficulty levels, and evaluate a broad set of frontier LLMs. Results show that the benchmark is highly discriminative, exposing large differences not only in success rate but also in interaction efficiency. Moreover, we empirically show that contextual perturbations cause moderate but consistent declines, whereas counterfactual revision and necessity judgment lead to much larger drops.