Randomly Wrong Signals: Bayesian Auction Design with ML Predictions
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.