We study auction design when a seller relies on machine-learning predictions of bidders' valuations that may be unreliable. Motivated by modern ML systems that are often accurate but occasionally fail in a way that is essentially uninformative, we model predictions as randomly wrong: with high probability the signal equals the bidder's true value, and otherwise it is a hallucination independent of the value. We analyze revenue-maximizing auctions when the seller publicly reveals these signals. A central difficulty is that the resulting posterior belief combines a continuous distribution with a point mass at the signal, so standard Myerson techniques do not directly apply. We provide a tractable characterization of the optimal signal-revealing auction by providing a closed-form characterization of the appropriate ironed virtual values. This characterization yields simple and intuitive implications. With a single bidder, the optimal mechanism reduces to a posted-price policy with a small number of regimes: the seller ignores low signals, follows intermediate signals, caps moderately high signals, and may again follow very high signals. With multiple bidders, we show that a simple eager second-price auction with signal-dependent reserve prices performs nearly optimally in numerical experiments and substantially outperforms natural benchmarks that either ignore the signal or treat it as fully reliable.
翻译:本研究探讨当卖方依赖可能不可靠的机器学习预测来估计投标人估值时的拍卖设计问题。受现代机器学习系统往往准确但偶尔会以完全无信息的方式失效这一现象启发,我们将预测建模为随机错误信号:以高概率信号等于投标人真实价值,否则信号为与价值无关的幻觉值。我们分析了卖方公开揭示这些信号时的收益最大化拍卖机制。核心难点在于由此产生的后验信念将连续分布与信号处的点质量相结合,导致标准迈尔森技术无法直接适用。通过给出适当熨平虚拟价值的闭式表征,我们为最优信号揭示拍卖提供了可处理的表征方法。该表征产生简单直观的结论:在单一投标人场景中,最优机制可简化为具有少量区间的挂牌价格策略——卖方忽略低信号、遵循中等信号、限制较高信号,并可能再次遵循极高信号。在多投标人场景中,数值实验表明采用信号依赖保留价的即时第二价格拍卖能实现近乎最优的性能,且显著优于忽略信号或将信号视为完全可靠的自然基准方法。