Anytime Contracts for AI Services

When organizations delegate text generation tasks to AI providers via pay-for-performance contracts, expected payments rise when evaluation is noisy. As evaluation methods become more elaborate, the economic benefits of decreased noise are often overshadowed by increased evaluation costs. In this work, we introduce adaptive contracts for AI delegation, which allow detailed evaluation to be performed selectively after observing an initial coarse signal in order to conserve resources. We make three sets of contributions: First, we provide efficient algorithms for computing optimal adaptive contracts under natural assumptions or when core problem dimensions are small, and prove hardness of approximation in the general unstructured case. We then formulate alternative models of randomized adaptive contracts and discuss their benefits and limitations. Finally, we empirically demonstrate the benefits of adaptivity over non-adaptive baselines using question-answering and code-generation datasets.

AI services incur inference costs during execution, while revenue may arrive later. Changing API prices, limited upfront capital, and service failures can limit operators' ability to sustain or expand their services. Beyond reducing per-request costs, operators need to plan future spending, fund execution before revenue arrives, and obtain compensation for specified losses. This requires clear agreements across services with different pricing and execution conditions. These agreements must distinguish rights to consume services from rights to receive payments, define obligations under uncertain costs and income, and specify which failures qualify for compensation and how much can be paid. We present TokenBank, a financial infrastructure that represents these commitments through structured contracts. It supports service-consumption rights, agreements that settle API-price differences in cash (forwards), financing through limited rights to future service revenue, and protection claims for specified service failures. Contracts specify participants, covered services, validity, ownership, fulfillment conditions, and settlement rules. Evaluation combines replay of 899,441 API requests, real model-driven agent execution, and contract API tests. In a zero-discount rising-price resampling scenario, forwards reduce mean expenditure by USD 304.88 but increase its standard deviation from USD 1,152.45 to USD 1,190.82. A controlled replication with five portfolios per capital condition finds mean contribution differences between financing and self-funding of +1.0635, -0.1406, and -0.2962 experimental USD under low, baseline, and ample capital, respectively. The evaluation distinguishes contract correctness from economic effectiveness under declared economic and failure assumptions; supplier invoices and commercial revenue are unavailable.

Test-time compute has emerged as a promising strategy to enhance the reasoning abilities of large language models (LLMs). However, this strategy has in turn increased how much users pay cloud-based providers offering LLM-as-a-service, since providers charge users for the amount of test-time compute they use to generate an output. In our work, we show that the market of LLM-as-a-service is socially inefficient: providers have a financial incentive to increase the amount of test-time compute, even if this increase contributes little to the quality of the outputs. To address this inefficiency, we introduce a reverse second-price auction mechanism where providers bid their offered price and (expected) quality for the opportunity to serve a user, and users pay proportionally to the marginal value generated by the winning provider relative to the second-highest bidder. To illustrate and complement our theoretical results, we conduct experiments with multiple instruct models from the $\texttt{Llama}$ and $\texttt{Qwen}$ families, as well as reasoning models distilled from $\texttt{DeepSeek-R1}$, on math and science benchmark datasets.