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.

Graph-SND: Sparse Aggregation for Behavioral Diversity in Multi-Agent Reinforcement Learning

System Neural Diversity (SND) measures behavioral heterogeneity in multi-agent reinforcement learning by averaging pairwise distances over all $\binom{n}{2}$ agent pairs, making each call quadratic in team size. We introduce Graph-SND, which replaces this complete-graph average with a weighted average over the edges of an arbitrary graph $G$. Three regimes follow: $G=K_n$ recovers SND exactly; a fixed sparse $G$ defines a localized diversity measure at $O(|E|)$ cost; and random edge samples yield an unbiased Horvitz-Thompson estimator and a normalized sample mean with $O(1/\sqrt{m})$ concentration in the sampled edge count $m$. For fixed sparse graphs we prove forwarding-index distortion bounds for expanders and a spectral refinement under low-rank distance structure; for random $d$-regular graphs we prove an unconditional probabilistic $\widetilde{\mathcal{O}}(D_{\max}/\sqrt{n})$ bound. On VMAS we verify recovery, unbiasedness, concentration, and wall-clock scaling, with a PettingZoo TVD panel checking non-Gaussian transfer. In a 500-iteration $n=100$ PPO run, Bernoulli-$0.1$ Graph-SND tracks full SND while reducing per-call metric time by about $10\times$, and frozen-policy GPU timing up to $n=500$ follows the predicted $\binom{n}{2}/|E|$ speedup. Random $d$-regular expanders empirically achieve $\mathrm{SND}_{G}^{\mathrm{u}}/\mathrm{SND} \in [0.9987, 1.0013]$ at $Θ(n \log n)$ edges. In DiCo diversity control at $n=50$, Bernoulli-$0.1$ Graph-SND preserves set-point tracking with paired reward differences indistinguishable from zero across nine matched cells while cutting per-call metric cost by ${\sim}9.5\times$. Together, these results show that the SND aggregation bottleneck can be removed without changing the metric's semantics, yielding a drop-in sparse alternative that scales beyond complete-graph SND and supports both passive measurement and closed-loop diversity control.

Stable Behavior, Limited Variation: Persona Validity in LLM Agents for Urban Sentiment Perception

Large Language Models (LLMs) are increasingly used as proxies for human perception in urban analysis, yet it remains unclear whether persona prompting produces meaningful and reproducible behavioral diversity. We investigate whether distinct personas influence urban sentiment judgments generated by multimodal LLMs. Using a factorial set of personas spanning gender, economic status, political orientation, and personality, we instantiate multiple agents per persona to evaluate urban scene images from the PerceptSent dataset and assess both within-persona consistency and cross-persona variation. Results show strong convergence among agents sharing a persona, indicating stable and reproducible behavior. However, cross-persona differentiation is limited: economic status and personality induce statistically detectable but practically modest variation, while gender shows no measurable effect and political orientation only negligible impact. Agents also exhibit an extremity bias, collapsing intermediate sentiment categories common in human annotations. As a result, performance remains strong on coarse-grained polarity tasks but degrades as sentiment resolution increases, suggesting that simple label-based persona prompting does not capture fine-grained perceptual judgments. To isolate the contribution of persona conditioning, we additionally evaluate the same model without personas. Surprisingly, the no-persona model sometimes matches or exceeds persona-conditioned agreement with human labels across all task variants, suggesting that simple label-based persona prompting may add limited annotation value in this setting.