Optimal Calibrated Signaling in Digital Auctions

TL;DR

This paper designs and characterizes optimal calibrated signaling mechanisms in digital ad auctions, enabling platforms to credibly disclose information that maximizes revenue while maintaining truthful bidder estimates.

Contribution

It provides a full characterization and efficient computation of the structure of optimal calibrated signals in second-price auctions, including surplus extraction and approximation algorithms.

Findings

Optimal signaling can extract or exceed full surplus.

The structure of optimal signals is fully characterized and efficiently computable.

An FPTAS is developed for approximate optimal signaling under IR constraints.

Abstract

In digital advertising, online platforms allocate ad impressions through real-time auctions, where advertisers typically rely on autobidding agents to optimize bids on their behalf. Unlike traditional auctions for physical goods, the value of an ad impression is uncertain and depends on the unknown click-through rate (CTR). While platforms can estimate CTRs more accurately using proprietary machine learning algorithms, these estimates/algorithms remain opaque to advertisers. This information asymmetry naturally raises the following questions: how can platforms disclose information in a way that is both credible and revenue-optimal? We address these questions through calibrated signaling, where each prior-free bidder receives a private signal that truthfully reflects the conditional expected CTR of the ad impression. Such signals are trustworthy and allow bidders to form unbiased value estimates, even without access to the platform's internal algorithms. We study the design of platform-optimal calibrated signaling in the context of second-price auction. Our first main result fully characterizes the structure of the optimal calibrated signaling, which can also be computed efficiently. We show that this signaling can extract the full surplus -- or even exceed it -- depending on a specific market condition. Our second main result is an FPTAS for computing an approximately optimal calibrated signaling that satisfies an IR condition. Our main technical contributions are: a reformulation of the platform's problem as a two-stage optimization problem that involves optimal transport subject to calibration feasibility constraints on the bidders' marginal bid distributions; and a novel correlation plan that constructs the optimal distribution over second-highest bids.