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.

翻译：我们研究了一个具有不可靠辅助信息的单一买家定价问题，其动机源于AI辅助决策和基于LLM的预测的日益普及。卖家观察到一个私人样本，该样本可能是准确的（与买家的估值一致），也可能是幻觉性的（从先验分布中独立抽取），但卖家不知道实际发生的是哪种情况。买家虽然未观察到实现的具体信号，却知道该信号是准确的还是幻觉性的。这造成了高阶信息不对称：卖家对自己辅助信息的可靠性不确定，而买家则拥有关于该可靠性的私有信息。采用一致性-鲁棒性框架，我们刻画了在一致性（准确信号下的性能）和鲁棒性（幻觉信号下的性能）之间权衡的精确帕累托前沿。我们表明，保留不可靠信号的私有性能够产生显著价值，其带来的权衡严格优于任何公共信号基准。我们进一步证明，完美的一致性并不排除对幻觉的有意义防护：对于每个先验分布，都存在一个机制，能够实现完美一致性并同时保证非平凡的鲁棒性$\frac{1}{2}$。此外，如果先验分布具有无限均值或均值不超过其垄断价格，我们提供了一个同时达到1-一致性和1-鲁棒性的机制。我们的结果展示了一种新的机制设计范式：机制不仅依赖设计者直接拥有的信息，还可以利用另一方关于设计者信息可靠性的知识来构建。