Keep, Customize, or Exit: Default Design and Token Pricing in LLM Reasoning Services

We study a large language model (LLM) service in which a provider chooses a per-token price and a default reasoning-token allocation, while a user may accept the default, customize the allocation, or exit. Larger allocations can improve accuracy but increase token cost and latency. We model this interaction as a Stackelberg game and derive the user's unique optimal customized allocation in closed form. For any price, the acceptable defaults form either an empty set or a compact interval. We characterize the provider's optimal default through a three-regime rule, reduce equilibrium computation to a one-dimensional price optimization, and prove the existence of the equilibrium. We further show that defaults affect the implemented reasoning allocation only when users value the convenience of avoiding customization; otherwise, every service-providing outcome implements the user's optimal customized allocation. Experiments with two compact open-weight reasoning models on five mathematics and science benchmarks support the accuracy-token model and show how model and task characteristics determine equilibrium prices, defaults, and reasoning allocations.

RUTA: Principled Visual Token Allocation via Rate-Utility Optimization

High-resolution images and long videos provide vision-language models with rich context for multimodal reasoning and fine-grained perception, but the resulting long visual token sequences make large language model-side computation and memory costly. Existing visual token reducers often operate at prescribed rates, while recent methods adapt token counts across inputs using method-specific learned thresholds or importance predictors. We introduce RUTA, a principled Rate-Utility Token Allocation method that performs pre-LLM reduction by jointly learning which tokens to retain and how many to allocate to each image-query pair. RUTA constructs query-conditioned candidate tokens and predicts a retention probability for each candidate. During training, these probabilities parameterize independent Bernoulli gates, while their sum provides a differentiable training-time estimate of the token count for each pair. Retained tokens serve as anchors that aggregate information from non-retained tokens according to semantic affinity and spatial proximity. RUTA is optimized with a penalized rate-utility objective that balances downstream task loss against expected token usage. Averaged across five benchmarks and measured relative to each backbone's full-token baseline, RUTA uses only $2.0\%$ and $4.2\%$ of visual tokens while preserving $88.2\%$ and $94.4\%$ of task performance on LLaVA-NeXT-7B and Qwen3-VL-8B, respectively.

Humans Disengage, Reasoning Models Persist: Separating Difficulty Registration from Deliberation Allocation

Large reasoning models (LRMs) take longer on harder problems, just as humans do. This surface similarity hides an opposite pattern within items. When an LRM gets a problem wrong, it spends more tokens than when it gets the same problem right; humans do the reverse, spending less time on the trials they get wrong. We separate two levels of deliberation: how response time tracks difficulty across items (registration), and, with item identity held fixed, whether an agent spends more on its own failures or successes (allocation). On a public matched human-LRM corpus, humans and all five thinking LRMs reproduce the known cross-item alignment (registration) but diverge within items (allocation): every LRM shows a large wrong-vs-right effect (Cohen's d = 1.47-3.13 on H-ARC) while humans show the opposite sign. The comparison stays inside each agent's own scale; we never put seconds and tokens on one axis. The dissociation holds under item fixed effects, replicates across datasets, and is absent in a non-thinking baseline. We read the human pattern as engagement versus abandonment: people stay on items they expect to solve and give up on the rest. We read the LRM pattern as length driven by uncertainty: chains grow when the model is unsure, which is exactly when it tends to fail. Both policies produce the same cross-item correlation with difficulty, so they look aligned on the measure prior work has used; the divergence shows up only once item identity is fixed. Under resource-rational metareasoning, the split is between two stopping policies that share a difficulty signal but implement opposite control; trace length captures the signal and misses the control.