# Error-Aware Reverse Auction Mechanism for Large Language Model Routing

arXiv: https://arxiv.org/abs/2608.12719 · HTML: https://mlsanity.com/paper/2608.12719/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 27 of 27)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [Router-R1: Teaching LLMs Multi-Round Routing and Aggregation via Reinforcement Learning](https://mlsanity.com/paper/2506.09033/) (2025)
- [EmbedLLM: Learning Compact Representations of Large Language Models](https://mlsanity.com/paper/2410.02223/) (2024)
- [Display Advertising with Real-Time Bidding (RTB) and Behavioural Targeting](https://mlsanity.com/paper/1610.03013/) (2016)
- [IRT-Router: Effective and Interpretable Multi-LLM Routing via Item Response Theory](https://mlsanity.com/paper/2506.01048/) (2025)
- [Real-time Bidding for Online Advertising: Measurement and Analysis](https://mlsanity.com/paper/1306.6542/) (2013)
- [AgentRouter: A Knowledge-Graph-Guided LLM Router for Collaborative Multi-Agent Question Answering](https://mlsanity.com/paper/2510.05445/) (2025)
- [ICL-Router: In-Context Learned Model Representations for LLM Routing](https://mlsanity.com/paper/2510.09719/) (2025)
- [Auctions with LLM Summaries](https://mlsanity.com/paper/2404.08126/) (2024)
- [An overview of domain-specific foundation model: key technologies, applications and challenges](https://mlsanity.com/paper/2409.04267/) (2024)
- [Ad Auctions for LLMs via Retrieval Augmented Generation](https://mlsanity.com/paper/2406.09459/) (2024)
- [Cached Model-as-a-Resource: Provisioning Large Language Model Agents for Edge Intelligence in Space-air-ground Integrated Networks](https://mlsanity.com/paper/2403.05826/) (2024)
- [Cost-Effective Communication: An Auction-based Method for Language Agent Interaction](https://mlsanity.com/paper/2511.13193/) (2025)
- [MTRouter: Cost-Aware Multi-Turn LLM Routing with History-Model Joint Embeddings](https://mlsanity.com/paper/2604.23530/) (2026)
- [COALESCE: Economic and Security Dynamics of Skill-Based Task Outsourcing Among Team of Autonomous LLM Agents](https://mlsanity.com/paper/2506.01900/) (2025)
- [Routing with Generated Data: Annotation-Free LLM Skill Estimation and Expert Selection](https://mlsanity.com/paper/2601.09692/) (2026)
- [QoEReasoner: An Agentic Reasoning Framework for Automated and Explainable QoE Diagnosis in RANs](https://mlsanity.com/paper/2606.01925/) (2026)

## Built on by (most cited first, 1 of 1)

- [Inference Auctions](https://mlsanity.com/paper/2609.40070/) (2026)

## Abstract (arXiv)

Routing each query to a cost-effective large language model (LLM) is critical for balancing quality and cost, yet most routers rely on a centralized task center to predict model performance, creating an information-risk mismatch and a scalability bottleneck as the model pool grows. We formulate LLM routing as a market-based allocation problem among strategic providers and propose a routing paradigm that shifts ex-ante prediction to LLM providers via a reverse auction, where providers submit self-predicted acceptance probabilities and execution costs. To account for noisy provider predictions and center evaluations, we introduce the textitError-Aware Reverse Auction Mechanism (EA-RAM), which explicitly models this Dual Error. We prove that, under a private-evaluation-belief structure, truthful effective-surplus reporting is incentive compatible in the reduced-form score space and individually rational under sellers' subjective beliefs, establish sufficient conditions for center rationality, and derive an explicit social-welfare loss bound. We further identify robustness effects: opposite-signed errors can cancel, vanishing-tail link functions (e.g., logistic) stabilize clear-cut cases via saturation, and extra noise smooths belief maps and reduces their maximal local sensitivity. Simulations and real-world benchmarks show that EA-RAM is robust to Dual Error and achieves a better cost--performance Pareto frontier than centralized baselines, with additional gains from provider-side local information, validating its practical effectiveness.