用机器学习预测竞标价时,如何设计让卖家收益最大化的拍卖机制。
Randomly Wrong Signals: Bayesian Auction Design with ML Predictions
- 将错误预测建模为随机失效的信号,结合真实价值与无关幻觉。
- 提出可计算的铁化虚拟值公式,实现最优公开信号拍卖。
- 单个竞标人时简化为分段定价,多竞标人时优于常见基准方法。
我们研究当卖方依赖可能不可靠的机器学习预测来估计竞标者估值时的拍卖设计问题。受现代机器学习系统常准确但偶尔以无信息方式失效的启发,我们将预测建模为‘随机错误’:高概率下信号等于真实估值,否则为独立于估值的幻觉。分析卖方公开这些信号时的收益最大化拍卖。核心难点在于后验信念同时包含连续分布和信号处的点质量,标准Myerson方法不适用。我们通过闭式表达铁化虚拟值,给出了最优信号公开拍卖的可计算刻画。该结果带来直观推论:单个竞标人时,最优机制退化为分段定价策略——忽略低信号、遵循中等信号、对中高信号设上限、可能再次采纳极高信号;多竞标人时,数值实验显示带信号相关保留价的简单激进第二价格拍卖近似最优,显著优于忽略信号或假设其完全可靠的自然基准。
原文摘要 · Abstract (English)
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.
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