Auctions with Interdependence and SOS: Improved Approximation

TL;DR

This paper presents a new randomized auction mechanism for interdependent values with SOS signals, achieving a tight 2-approximation to optimal welfare in binary signal settings, improving upon previous 4-approximation results.

Contribution

It introduces a truthful, randomized auction mechanism that improves welfare approximation from 4 to 2 for binary signals under SOS conditions.

Findings

Achieves a tight 2-approximation for welfare with binary signals.

Mechanism is truthful and randomized, assigning 0 or 0.5 probabilities.

Results extend to matroid settings.

Abstract

Interdependent values make basic auction design tasks -- in particular maximizing welfare truthfully in single-item auctions -- quite challenging. Eden et al. recently established that if the bidders valuation functions are submodular over their signals (a.k.a. SOS), a truthful 4-approximation to the optimal welfare exists. We show existence of a mechanism that is truthful and achieves a tight 2-approximation to the optimal welfare when signals are binary. Our mechanism is randomized and assigns bidders only 0 or 0.5 probabilities of winning the item. Our results utilize properties of submodular set functions, and extend to matroid settings.