Optimal Pricing with Unreliable Signals

2026-04-03

AI Summary

This study addresses optimal pricing by a seller facing a single buyer when the seller possesses an unreliable signal—potentially accurate or hallucinated—about the buyer’s valuation, while the buyer privately knows the signal’s reliability, creating higher-order information asymmetry. The work proposes a novel mechanism design paradigm that bypasses the seller’s uncertainty about signal reliability by leveraging the buyer’s private knowledge thereof. Building on Bayesian mechanism design and a trade-off analysis between consistency and robustness, the authors construct an optimal pricing mechanism under private signals that strictly outperforms the benchmark with public signals. Key contributions include characterizing the exact Pareto frontier between consistency and robustness, constructing—for any prior distribution—a mechanism that is 1-consistent and at least 1/2-robust, and achieving simultaneous 1-consistency and 1-robustness when the prior mean is no greater than the monopoly price or tends to infinity.

Abstract

We study a single-buyer pricing problem with unreliable side information, motivated by the increasing use of AI-assisted decision-making and LLM-based predictions. The seller observes a private sample that may be either accurate (coinciding with the buyer's valuation), or hallucinatory (an independent draw from the prior), without knowing which case has realized. The buyer does not observe the realized signal, yet knows whether it is accurate or hallucinatory. This creates a higher-order informational asymmetry: the seller is uncertain about the reliability of his own side information, while the buyer has private information about that reliability. Adopting a consistency-robustness framework, we characterize the exact Pareto frontier of tradeoffs between consistency (performance under an accurate signal) and robustness (performance under a hallucinatory signal). We show that keeping the unreliable signal private generates substantial value, yielding tradeoffs that strictly dominate any public-signal benchmark. We further show that perfect consistency does not preclude meaningful protection against hallucination: for every prior, there exists a mechanism achieving perfect consistency together with a nontrivial robustness guarantee of $\frac{1}{2}$. Moreover, if the prior has an infinite mean or a mean of at most its monopoly price, we provide a mechanism that is simultaneously 1-consistent and 1-robust. Our results illustrate a new mechanism design paradigm: rather than relying only on information directly possessed by the designer, mechanisms can be built to leverage the other side's knowledge about the reliability of the designer's information.

Problem

• unreliable signals
• pricing mechanism
• information asymmetry
• consistency-robustness tradeoff
• AI-assisted decision-making

Innovation

• unreliable signals
• consistency-robustness tradeoff
• information asymmetry
• mechanism design
• private signaling