Calibrated Click-Through Auctions: An Information Design Approach

TL;DR

This paper investigates how to optimally design information about click-through rates in auctions to maximize efficiency and surplus, using an information design approach with calibrated signals.

Contribution

It introduces a novel framework for designing optimal unbiased estimators of click-through rates under calibration constraints in auction settings.

Findings

Optimal information structures achieve social efficiency and surplus extraction.

Private and correlated signals are necessary for optimal design.

Partial information disclosure is optimal in asymmetric settings.

Abstract

We analyze the optimal information design in a click-through auction with fixed valuations per click, but stochastic click-through rates. While the auctioneer takes as given the auction rule of the click-through auction, namely the generalized second-price auction, the auctioneer can design the information flow regarding the click-through rates among the bidders. A natural requirement in this context is to ask for the information structure to be calibrated in the learning sense. With this constraint, the auction needs to rank the ads by a product of the bid and an unbiased estimator of the click-through rates, and the task of designing an optimal information structure is thus reduced to the task of designing an optimal unbiased estimator. We show that in a symmetric setting with uncertainty about the click-through rates, the optimal information structure attains both social efficiency and surplus extraction. The optimal information structure requires private (rather than public) signals to the bidders. It also requires correlated (rather than independent) signals, even when the underlying uncertainty regarding the click-through rates is independent. Beyond symmetric settings, we show that the optimal information structure requires partial information disclosure.