A Duality-Based Unified Approach to Bayesian Mechanism Design

TL;DR

This paper introduces a duality framework for Bayesian mechanism design that unifies various approaches, leading to new insights and improved approximation guarantees for revenue maximization in auction settings.

Contribution

It presents a duality-based unified approach that encompasses multiple existing methods and yields better approximation ratios for revenue guarantees.

Findings

A duality framework for Bayesian mechanism design is developed.

Posted-price mechanisms and VCG auctions achieve constant-factor approximations.

Improved approximation ratios from 30 to 24 and 69 to 8 for specific auction types.

Abstract

We provide a unified view of many recent developments in Bayesian mechanism design, including the black-box reductions of Cai et al. [CDW13b], simple auctions for additive buyers [HN12], and posted-price mechanisms for unit-demand bidders [CHK07]. Additionally, we show that viewing these three previously disjoint lines of work through the same lens leads to new developments as well. First, we provide a duality framework for Bayesian mechanism design, which naturally accommodates multiple agents and arbitrary objectives/feasibility constraints. Using this, we prove that either a posted-price mechanism or the Vickrey-Clarke-Groves auction with per-bidder entry fees achieves a constant-factor of the optimal revenue achievable by a Bayesian Incentive Compatible mechanism whenever buyers are unit-demand or additive, unifying previous breakthroughs of Chawla et al. [CHMS10] and Yao [Yao15], and improving both approximation ratios (from 30 to 24 and 69 to 8, respectively). Finally, we show that this view also leads to improved structural characterizations in the Cai et al. framework.