Auctions with price predictions

We study auctions for unlimited-supply goods in which the seller receives a single prediction of the revenue-maximizing uniform price. Comparing with the uniform-price benchmarks $\mathcal F$ and $\mathcal{F}^{(2)}$ for consistency and robustness respectively, we show that every universally truthful bid-independent mechanism with consistency $c$ and robustness $r$ satisfies $ c+\lambda_n r\le 1, $ where $\lambda_n$ is the optimal approximation ratio for $n$ bidders against $\mathcal{F}^{(2)}$ without predictions. Equality is achieved by a family of simple mechanisms that randomize between offering the predicted price and running an optimal prior-free auction. We then study imperfect advice when the mechanism receives a point prediction without any knowledge of its error. We extend our consistency-robustness bound to incorporate an arbitrary regular monotone graceful-degradation profile under prediction overestimates and design error-unaware mechanisms that achieve the resulting frontier. Finally, we study how a price prediction can be learned from historical markets, proving a tight $\Theta(\log n)$ pseudo-dimension bound for shared-price revenue and an $O(d_{\mathcal H}\log n)$ bound for the revenue for contextual price predictors with pseudo-dimension $d_{\mathcal H}$. Together, our results give an end-to-end account of how a price prediction can be learned and used robustly.