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 propose a market-based routing paradigm that shifts ex-ante prediction to LLM providers via a reverse auction, where providers bid with self-predicted success probabilities and execution costs.

To account for inherently noisy provider predictions and center evaluations, we introduce the Error-Aware Reverse Auction Mechanism (EA-RAM), which explicitly models this inherent Dual Error. We prove that EA-RAM is Bayesian incentive compatible and individually rational under the Dual Error, establish sufficient conditions for center rationality, and derive an explicit 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, reducing the gains from marginal manipulation. Experiments on simulations and real-world benchmarks show that EA-RAM is robust to the Dual Error and achieves a better cost--performance Pareto frontier than centralized baselines, with additional gains when providers contribute local information, validating its practical effectiveness.