Test-Time Compute Games

• URL: http://arxiv.org/abs/2601.21839v1
• Date: Thu, 29 Jan 2026 15:18:01 GMT
• Title: Test-Time Compute Games
• Authors: Ander Artola Velasco, Dimitrios Rontogiannis, Stratis Tsirtsis, Manuel Gomez-Rodriguez,
• Abstract summary: Test-time compute has emerged as a promising strategy to enhance the reasoning abilities of large language models.<n>We show that the market of LLM-as-a-service is socially inefficient, since providers have a financial incentive to increase the amount of test-time compute.<n>We introduce a reverse second-price auction mechanism where providers bid their offered price and (expected) quality for the opportunity to serve a user.
• Score: 11.108199754300772
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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