VCG Under False-name Attacks: a Bayesian Analysis

TL;DR

This paper analyzes the vulnerability of the VCG auction to false-name attacks in a Bayesian context, introducing a new concept called the granularity threshold to characterize its resilience.

Contribution

It introduces the granularity threshold to evaluate VCG's Bayesian resilience to false-name attacks and identifies cases where VCG remains robust.

Findings

VCG can be Bayesian resilient in certain two-item single-minded settings.

The granularity threshold effectively characterizes VCG's resilience.

Many cases show VCG's robustness against false-name attacks.

Abstract

VCG is a classical combinatorial auction that maximizes social welfare. However, while the standard single-item Vickrey auction is false-name-proof, a major failure of multi-item VCG is its vulnerability to false-name attacks. This occurs already in the natural bare minimum model in which there are two identical items and bidders are single-minded. Previous solutions to this challenge focused on developing alternative mechanisms that compromise social welfare. We re-visit the VCG auction vulnerability and consider the bidder behavior in Bayesian settings. In service of that we introduce a novel notion, termed the granularity threshold, that characterizes VCG Bayesian resilience to false-name attacks as a function of the bidder type distribution. Using this notion we show a large class of cases in which VCG indeed obtains Bayesian resilience for the two-item single-minded setting.