On Robustness to $k$-wise Independence of Optimal Bayesian Mechanisms

TL;DR

This paper investigates how the optimal Bayesian auction mechanisms perform under relaxed independence assumptions, revealing that Myerson's mechanism is not robust to pairwise independence but is robust under 3-wise independence, while second-price auctions maintain revenue guarantees.

Contribution

It provides a detailed analysis of the robustness of classic auction mechanisms to different levels of independence assumptions in priors.

Findings

Myerson's mechanism loses nearly all revenue under pairwise independence.

Myerson's mechanism is robust under 3-wise independence.

Second-price auctions with reserves retain a constant fraction of revenue under pairwise independence.

Abstract

This paper reexamines the classic problem of revenue maximization in single-item auctions with $n$ buyers under the lens of the robust optimization framework. The celebrated Myerson's mechanism is the format that maximizes the seller's revenue under the prior distribution, which is mutually independent across all $n$ buyers. As argued in a recent line of work (Caragiannis et al. 22), (Dughmi et al. 24), mutual independence is a strong assumption that is extremely hard to verify statistically, thus it is important to relax the assumption. While optimal under mutual independent prior, we find that Myerson's mechanism may lose almost all of its revenue when the independence assumption is relaxed to pairwise independence, i.e., Myerson's mechanism is not pairwise-robust. The mechanism regains robustness when the prior is assumed to be 3-wise independent. In contrast, we show that second-price auctions with anonymous reserve, including optimal auctions under i.i.d. priors, lose at most a constant fraction of their revenues on any regular pairwise independent prior. Our findings draw a comprehensive picture of robustness to $k$-wise independence in single-item auction settings.