Simple and Nearly Optimal Multi-Item Auctions

TL;DR

This paper presents a polynomial time approximation scheme for nearly optimal multi-item auctions with independent bidders and valuations, using simple auction mechanisms like second-price or VCG, achieving results previously unknown even for single bidders.

Contribution

It introduces a PTAS for Bayesian multi-item multi-bidder auctions under broad conditions, using simple auction rules, advancing beyond prior constant-factor approximations.

Findings

PTAS achieved for non-i.i.d. bidders with additive valuations

Simple auction mechanisms suffice for near-optimal revenue

Applicable to small numbers of bidders with non-i.i.d. distributions

Abstract

We provide a Polynomial Time Approximation Scheme (PTAS) for the Bayesian optimal multi-item multi-bidder auction problem under two conditions. First, bidders are independent, have additive valuations and are from the same population. Second, every bidder's value distributions of items are independent but not necessarily identical monotone hazard rate (MHR) distributions. For non-i.i.d. bidders, we also provide a PTAS when the number of bidders is small. Prior to our work, even for a single bidder, only constant factor approximations are known. Another appealing feature of our mechanism is the simple allocation rule. Indeed, the mechanism we use is either the second-price auction with reserve price on every item individually, or VCG allocation with a few outlying items that requires additional treatments. It is surprising that such simple allocation rules suffice to obtain nearly optimal revenue.