Test-Time Compute Games
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915989827878912 |
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| author | Velasco, Ander Artola Rontogiannis, Dimitrios Tsirtsis, Stratis Gomez-Rodriguez, Manuel |
| author_facet | Velasco, Ander Artola Rontogiannis, Dimitrios Tsirtsis, Stratis Gomez-Rodriguez, Manuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21839 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Test-Time Compute Games Velasco, Ander Artola Rontogiannis, Dimitrios Tsirtsis, Stratis Gomez-Rodriguez, Manuel Computers and Society Artificial Intelligence Computer Science and Game Theory Machine Learning 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. |
| title | Test-Time Compute Games |
| topic | Computers and Society Artificial Intelligence Computer Science and Game Theory Machine Learning |
| url | https://arxiv.org/abs/2601.21839 |