Mentalization - the ability to infer others' beliefs and intentions to guide one's own choices - is a key cognitive function underlying human social interactions. Large language models (LLMs) demonstrate behaviour consistent with humans on theory-of-mind tasks, yet whether these models can guide adaptive behaviour through mentalization is unknown. Here we use two economic games with cognitive computational modeling to uncover the latent strategies underlying mentalization in LLMs. We tested individual LLM agents across four model families, DeepSeek, GPT-4.1, GPT-5 and Gemini 2.0 Flash (N = 2,099), against opponents of varying sophistication and examined whether a prompting strategy designed to elicit strategic reasoning improved performance. We benchmarked results against human participants (N = 251) as a comparative measure. Across both games, LLMs showed clear behavioural and computational signatures of mentalizing that differed markedly by model provider and size. Strategic prompting generally improved performance by inducing more sophisticated reasoning, yet the extent of the benefit differed across the two tasks. Last, GPT-5 agents flexibly adapted their recursive depth of reasoning to increasingly sophisticated opponents, demonstrating superior performance to human participants. Collectively, we demonstrate different capacities for mentalization across LLMs, and highlight cognitive computational modeling as a formal method for assessing comparative intelligence across humans and machines.
Strategic reasoning in Large Language Models (LLMs) within long-horizon environments is often limited by inconsistent subgoals. In these settings, finite attention resources prevent the model from maintaining strategic coherence over thousands of steps. This limitation leads to strategic drift, where localized decisions fail to sustain a coherent trajectory across reasoning. To address this, we introduce EpicStar, a framework that enables agents to learn memory as policy to tackle long-horizon reasoning. Specifically, the agent maintains a bank of successful past episodes as a heuristic alongside a working memory to track short-term environmental changes. During inference, a dynamic gating mechanism determines whether to execute a retrieved action directly or to perform new reasoning through a contextual fusion of the retrieved episodes and current working memory. Utilizing StarCraft II as the testbed, we evaluated EpicStar against diverse opponent styles. It significantly outperforms baseline methods, achieving higher win rates while consuming an order of magnitude fewer tokens, and it maintains this advantage consistently across difficulty levels and opponent strategies. Our findings provide compelling evidence that structured cross-episode memory is essential for enabling LLM agents to perform robust, long-term strategic execution in dynamic, autonomous settings.
Joshua Caiata, Sreepriya Pulyassary, Xiang Li +1cs.GT cs.AI cs.LG cs.MA
Learning a strategic task changes more than what is directly taught: fine-tuning on one game can either enhance or degrade an agent's ability to reason in another. Understanding and predicting this transfer of strategic capabilities, however, remains a key challenge for large language models (LLMs). Normal-form games provide an ideal testbed for analyzing this phenomenon, as they feature explicitly defined payoffs and well-characterized equilibrium behaviours. In this work, we investigate whether game embeddings can explain and predict changes in LLM strategic capabilities following fine-tuning across different games. We propose a lightweight two-feature embedding that captures fundamental behavioural demands: the entropy of the Nash equilibrium and the sensitivity of optimal responses to an opponent's action. We show that while existing published structural embeddings primarily memorize game identities and fail to generalize, our behavioural embedding reliably predicts performance changes on held-out games. These results demonstrate that the transfer of strategic capabilities in LLMs is not dictated by the payoff geometry of a game, but by the underlying structure of the decision-making behaviour it requires.
We introduce Age of LLM, a turn-based 1v1 benchmark in which two LLMs face off on a 13x7 grid to destroy the enemy base. Three stressors are deliberate: fog of war, full diplomacy (messages, ceasefires, ultimatums; uranium kept secret), and a reliability dimension where every turn must follow a strict JSON schema and an illegal action is silently discarded. The engine is private and each match uses a fresh random map seed and opponent, mitigating the data contamination that affects public benchmarks. Models receive a (near) rule-only prompt with no build-order advice (two tactical seed phrases were present during data collection; see Section 2.7). We benchmark 15 reasoning models across 54 matches and 5,258 actions. Findings: (1) the nuclear rush dominates (78% on the rules-coherent v0.11+ sub-corpus; 85% corpus-wide) with a sole-launcher signature that is largely mechanical under secret-simultaneous launch rules, not a cognitive deterrence failure; (2) military conquest is rare but faster (12.3 vs 18.9 turns); (3) diplomacy is prolific yet almost never consummated; (4) ~58% of illegal actions are fog/state errors, making the illegal-action rate a measure of belief-tracking; (5) -- the least established, and the only one we label exploratory -- a weak link associates reliability with winning. The corpus is small, unbalanced and not side-swapped, so the ranking is a preliminary descriptive view, not a contribution. Beyond ranking, the turn-by-turn traces of actions and messages make the corpus a lens on how LLMs reason under adversarial uncertainty -- their belief-tracking, spontaneous deception, and per-model cognitive "personas" -- which we frame as a future research direction. We release the replay format, an isometric viewer and all replays; engine source on request.
Strategic reasoning under uncertainty underpins consequential decisions in negotiation, finance, and policy, but prevailing game-play benchmarks collapse heterogeneous reasoning dimensions into a single scalar, leaving the capability structure of frontier LLMs unexamined. We introduce Poker Arena, a no-limit Texas Hold'em tournament platform that couples a three-layer memory architecture (within-hand, session, and cross-session) with a nine-axis cognitive profile decomposing strategic reasoning into interpretable dimensions such as bet-sizing calibration and positional awareness. We evaluate seven frontier models across 50 sessions of 1,000 hands and a controlled memory ablation; tournament chips and aggregate axis score order the field differently: Claude Opus 4.6 wins +$15,730 chips with 14 first-place finishes, yet ranks only fifth of seven on mean axis score, while persistent memory helps some models and hurts others. These findings show that multi-axis evaluation surfaces capability structure that scalar leaderboards systematically misrank, with cross-dimensional consistency outweighing peak performance on any single axis.
Static benchmarks capture only part of how large language models behave in practice. Real systems place models inside repeated loops with time limits, formatting constraints, and failure modes. We study this setting in a timed multi-phase Risk environment with explicit victory targets and repeated planning and execution cycles. In a replicated 32-game cross-provider championship under frozen rules, gemini-3.1-pro-preview won 20 of 32 games against gpt-5.1, claude-opus-4-7, and kimi-k2.6, and the pooled winner distribution differs strongly from an equal-strength null (p approx 1.5 x 10^-5). We then separate planning from execution by standardizing execution on a cheaper Gemini Flash scaffold. Under this design, a pooled 32-game planner bakeoff is consistent with near-equality (p approx 0.821), which indicates that much of the earlier provider spread came from end-to-end system behavior rather than planning alone. To study mechanism, we analyze saved planning and execution traces from the provider championship. Gemini refers to the terminal objective far more often than the other models and increases that focus as victory approaches. Gemini also converts more turns into deep conquest chains, even though it is not the cleanest runtime. These results show that live-agent performance depends on objective tracking, execution conversion, cost, and runtime reliability, and they support evaluating LLMs as components in bounded workflows rather than as isolated benchmark respondents.
While Large Language Models (LLMs) excel in certain reasoning tasks, they struggle in multi-agent games where the final outcome depends on the joint strategies of all agents. In multi-agent games, the non-stationarity of other agents brings significant challenges on the evaluation of the reasoning process and the credit assignment over multiple reasoning steps. Existing single-agent reinforcement learning (RL) approaches and their multi-agent extensions fail to address these challenges as they do not incorporate other agents in the reasoning process. In this work, we propose Strat-Reasoner, a novel RL-based framework that improves LLMs' strategic reasoning ability in multi-agent games. We introduce a novel recursive reasoning paradigm where an agent's reasoning also integrates other agents' reasoning processes. To provide effective reward signals for the intermediate reasoning sequences, we employ a centralized Chain-of-Thought (CoT) comparison module to evaluate the reasoning quality. Finally, we compute an accurate hybrid advantage and develop a group-relative RL approach to optimize the LLM policy. Experimental results show that Strat-Reasoner substantially improves strategic abilities of underlying LLMs, achieving 22.1\% average performance improvements across various multi-agent games.