Test-Time Compute Games

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Velasco, Ander Artola, Rontogiannis, Dimitrios, Tsirtsis, Stratis, Gomez-Rodriguez, Manuel
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915989827878912
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