Position: Profiling Game Worlds by Transition Complexity

When Reasoning Narrows the Move: Diversity Collapse in LLM Game Play

Supervised fine-tuning (SFT) is widely used to adapt large language models to downstream tasks, but its effect on behavioral diversity in sequential decision-making remains under-explored. We study this question in a controlled suite of deterministic board games based on tic-tac-toe variants, where optimal actions are exactly computable and diversity can be measured directly. Across state-level evaluation, arena gameplay, and training trajectories, we find that reasoning-mode generation frequently suppresses action diversity without uniformly improving action accuracy. Furthermore, standard SFT improves accuracy but often induces premature diversity collapse, which exceeds what is minimally required by the accuracy-diversity tradeoff. We then show that action augmentation, which trains on all optimal actions per state rather than a single demonstrated action, would partially mitigates this effect. Our results identify narrow-support imitation as a source of policy collapse in LLM decision-making and suggest that preserving action support during SFT is important for maintaining exploratory behavior.

Beyond Asking: A Pipeline for Personalized Game Generation that Reads Players from Behavior

Personalized game generation requires inferring a player's abilities and behavioral style from how they play. Large language models have made this inference more attainable than ever: an LLM can read a raw gameplay transcript and produce a fluent, plausible profile of the player. Plausible, however, is not verified, and verification is precisely what the field lacks: latent traits are unobservable; questionnaires provide noisy proxies and become circular when self-reports are used to validate behavior-based inference; and behavior itself is ambiguous without context -- a player who never collects an item may not want it, or may never have had the chance. We address both problems. First, we construct a synthetic player population whose traits are ground truth by construction: each trait is an explicit bot parameter, accepted only after controlled manipulation produces consistent, trait-specific behavioral change. Unlike prior parameter-recovery work that inverts a known decision model, our benchmark evaluates policy-agnostic inference from behavioral transcripts alone. Second, we introduce an opportunity-aware decision-moment representation that disentangles preference from the chance to express it; ablating it selectively degrades opportunity-dependent traits. On this benchmark, few-shot LLM inference outperforms embedding- and rule-based baselines on most traits, though feature-based supervised regressors remain stronger overall. Finally, we close the loop: inferred profiles drive difficulty adaptation, evaluated against ground-truth references and mismatched-profile controls, and an exploratory human study examines whether these findings transfer to real players.

Generative Gamer: Learning Equilibrium Strategy by LLM-driven Dynamic Deduction

Large Language Models (LLMs) have demonstrated remarkable general capabilities, yet they falter in domains requiring deep strategic reasoning. A primary obstacle is the need to navigate a game tree that grows exponentially with search depth, a task for which their generative nature is ill-suited. To address this, we introduce Generative Gamer (GenGamer), a framework that trains LLMs to reason like an expert player. Instead of attempting an exhaustive search, GenGamer learns to generate a compact, pruned reasoning trajectory termed as a Dynamic Deduction. This is achieved by integrating three key strategies: action pruning based on policy confidence, state pruning via value estimation, and branch pruning inspired by alpha-beta principles. Furthermore, to train the model effectively, we propose the Deduction Tree Reward (DTR), a process-oriented mechanism that provides step-by-step feedback on the quality of the reasoning process, rather than relying solely on the final game outcome. Experiments on complex games such as Tic-Tac-Toe and Leduc Poker demonstrate that GenGamer significantly enhances the strategic capabilities of LLMs, enabling them to achieve performance that surpasses current state-of-the-art language models.

RevengeBench: Reverse Engineering Code-Space Policies from Behavioral Experiments

For most of scientific history, researchers studying behavior could only infer hidden mechanisms from outward actions: an inverse problem that becomes more tractable when observation is augmented by targeted intervention. We pose a computational analogue: given only behavioral traces of an agent in a game environment, can a learner reconstruct the underlying decision program as executable code, and how much does this reconstruction improve with the ability to design controlled experiments? We introduce RevengeBench, a benchmark of 75 LLM generated, Elo-calibrated policies across five game environments, drawn from CodeClash tournament trajectories. The learner observes the hidden target policy play against sampled opponents and designs behavioral probes in the form of custom opponent policies that elicit informative behavior. It then submits an executable hypothesis, which is evaluated using continuous action-distance metrics. We further validate that recovered code carries informative signal in downstream player-versus-player tournaments. Across twelve frontier LLMs, recovery quality varies substantially (34 to 72% of initial distance closed), with reconstructed policies yielding measurable competitive advantage, particularly for weaker models that otherwise struggle to design effective counter-strategies. Our benchmark positions behavioral recovery of programmatic policies as a tractable inverse problem in code-space, opening a path to opponent modeling, policy interpretability, and the broader question of inferring latent mechanisms from observations.

Post-Training at the Edge of Detectability: A Game-Theoretic Approach to Fine-Tuning

Reinforcement learning (RL) fine-tuning is widely used in language model training to improve model performance on a target task while limiting drift from a reference policy. A standard way to balance this trade-off is via a KL-regularized RL objective, although this formulation does not by itself provide a principled way to set the regularization coefficient. In practice, the coefficient is typically chosen heuristically or via hyperparameter search, which can lead to unnecessary overhead in training cost or undesirable reward-retention trade-offs. We instead propose a game-theoretic framework that gives this trade-off an explicit statistical interpretation. Specifically, we study a sequential game in which an agent chooses a policy to maximize cumulative reward while a monitor observes policy outputs over time and tests for deviations from the reference policy. Although not originating from the same perspective, we show that the resulting equilibrium policy can nonetheless be expressed as the solution to a KL-regularized RL problem for an optimal regularization parameter that can be viewed as maximizing reward per unit of statistical distinguishability. Drawing on classical results from concave-convex fractional programming, we provide a principled method for learning this equilibrium coefficient via reduction to the KL-regularized RL objective, thus allowing for flexible integration into standard fine-tuning pipelines. In experiments with Qwen3-8B and Llama-3.2-1B, we demonstrate that our methods result in competitive reward-retention trade-offs in a continual learning setting, and illustrate how our framework may be used to audit API providers serving open-source models.

Scaling Test-Time Compute via Generative Verification in Constrained Parameter Regimes