Bayesian Incentive Compatibility via Fractional Assignments

TL;DR

This paper extends a black-box reduction technique to multi-parameter Bayesian mechanism design with finite support priors, enabling the creation of approximately incentive-compatible mechanisms with minimal social welfare loss.

Contribution

It introduces a black-box reduction for multi-parameter Bayesian mechanisms with finite support priors, achieving eps-BIC mechanisms with constant approximation for combinatorial auctions.

Findings

Provides a reduction converting any algorithm into an eps-BIC mechanism.

Achieves constant approximation in combinatorial auctions with sub-additive agents.

Maintains social welfare close to the original algorithm.

Abstract

Very recently, Hartline and Lucier studied single-parameter mechanism design problems in the Bayesian setting. They proposed a black-box reduction that converted Bayesian approximation algorithms into Bayesian-Incentive-Compatible (BIC) mechanisms while preserving social welfare. It remains a major open question if one can find similar reduction in the more important multi-parameter setting. In this paper, we give positive answer to this question when the prior distribution has finite and small support. We propose a black-box reduction for designing BIC multi-parameter mechanisms. The reduction converts any algorithm into an eps-BIC mechanism with only marginal loss in social welfare. As a result, for combinatorial auctions with sub-additive agents we get an eps-BIC mechanism that achieves constant approximation.