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

Supervised Fine-Tuning (SFT) is essential for aligning Large Language Models (LLMs) with user intent, yet it is believed to suppress generative diversity. Although this reduction is frequently referenced, formal empirical testing of the phenomenon remains limited. The expressiveness of LLMs by itself was addressed by multiple prior methods. Their varying perspectives suggest that deeper investigation could yield further improvements. In this study, we attribute the decline to two primary drivers: the neglect of low-frequency patterns within fine-tuning datasets and the forgetting of preexisting knowledge. Motivated by our theoretical analysis, we develop Tempered Focal (TOFU) loss, a novel objective that addresses both stated challenges simultaneously. Our extensive evaluation confirms at scale that generation breadth narrows after SFT and strengthens the hypothesis explaining this effect. Across multiple models and benchmarks, we demonstrate that TOFU enhances output diversity while preserving high response quality, offering a principled approach to SFT.

Large language models have improved substantially on single-shot reasoning tasks, but their performance in sequential decision-making is less well understood. We study this on fully-observable two-player zero-sum games, which provide ground-truth evaluation: outcomes are determined by the rules, and optimality of individual moves can be computed or approximated, without relying on a judge model. Across model tiers, LLMs play suboptimally in simple games such as tic-tac-toe or Connect Four, and lose to MCTS opponents. Obfuscations that preserve the game tree but rewrite its surface form leave performance largely unchanged, indicating the gap is not fully explained by recall of memorized strategies. Motivated by this performance gap, we introduce an agentic framework enhanced with an experience memory designed for the sequential setting and addressing common challenges of sequential decision-making such as credit assignment. We show that post-game reflection and rule extraction yield measurable improvements on tic-tac-toe without modifying the model weights.

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.