Public Signaling in Bayesian Ad Auctions

TL;DR

This paper investigates how to optimally send public signals in Bayesian ad auctions with multiple slots to maximize revenue, providing algorithms under various constraints and analyzing computational complexity.

Contribution

It introduces the first study of signaling in multi-slot Bayesian ad auctions, offering polynomial-time algorithms and approximation schemes under specific conditions.

Findings

The signaling problem is NP-hard in general.

Polynomial-time solutions exist when the number of states or slots is fixed.

Approximation schemes are available for single-minded bidders and certain valuation distributions.

Abstract

We study signaling in Bayesian ad auctions, in which bidders' valuations depend on a random, unknown state of nature. The auction mechanism has complete knowledge of the actual state of nature, and it can send signals to bidders so as to disclose information about the state and increase revenue. For instance, a state may collectively encode some features of the user that are known to the mechanism only, since the latter has access to data sources unaccessible to the bidders. We study the problem of computing how the mechanism should send signals to bidders in order to maximize revenue. While this problem has already been addressed in the easier setting of second-price auctions, to the best of our knowledge, our work is the first to explore ad auctions with more than one slot. In this paper, we focus on public signaling and VCG mechanisms, under which bidders truthfully report their valuations. We start with a negative result, showing that, in general, the problem does not admit a PTAS unless P = NP, even when bidders' valuations are known to the mechanism. The rest of the paper is devoted to settings in which such negative result can be circumvented. First, we prove that, with known valuations, the problem can indeed be solved in polynomial time when either the number of states d or the number of slots m is fixed. Moreover, in the same setting, we provide an FPTAS for the case in which bidders are single minded, but d and m can be arbitrary. Then, we switch to the random valuations setting, in which these are randomly drawn according to some probability distribution. In this case, we show that the problem admits an FPTAS, a PTAS, and a QPTAS, when, respectively, d is fixed, m is fixed, and bidders' valuations are bounded away from zero.