Revelation Gap for Pricing from Samples

TL;DR

This paper investigates the limitations of truthful mechanisms in prior-independent auction design, revealing a significant gap between truthful and non-truthful mechanisms in revenue approximation for single-item sales.

Contribution

It identifies and quantifies the revelation gap for revenue maximization, demonstrating that non-truthful mechanisms can outperform truthful ones in prior-independent settings.

Findings

Sample-bid mechanism achieves approximation ratios of 1.835 (regular) and 1.296 (MHR)

No truthful mechanism can surpass approximation ratios of 1.957 (regular) and 1.543 (MHR)

Non-truthful mechanisms can outperform truthful mechanisms, establishing a non-trivial revelation gap.

Abstract

This paper considers prior-independent mechanism design, in which a single mechanism is designed to achieve approximately optimal performance on every prior distribution from a given class. Most results in this literature focus on mechanisms with truthtelling equilibria, a.k.a., truthful mechanisms. Feng and Hartline (2018) introduce the revelation gap to quantify the loss of the restriction to truthful mechanisms. We solve a main open question left in Feng and Hartline (2018); namely, we identify a non-trivial revelation gap for revenue maximization. Our analysis focuses on the canonical problem of selling a single item to a single agent with only access to a single sample from the agent's valuation distribution. We identify the sample-bid mechanism (a simple non-truthful mechanism) and upper-bound its prior-independent approximation ratio by 1.835 (resp. 1.296) for regular (resp. MHR) distributions. We further prove that no truthful mechanism can achieve prior-independent approximation ratio better than 1.957 (resp. 1.543) for regular (resp. MHR) distributions. Thus, a non-trivial revelation gap is shown as the sample-bid mechanism outperforms the optimal prior-independent truthful mechanism. On the hardness side, we prove that no (possibly non-truthful) mechanism can achieve prior-independent approximation ratio better than 1.073 even for uniform distributions.