Welfare-Preserving $\varepsilon$-BIC to BIC Transformation with Negligible Revenue Loss

TL;DR

This paper introduces a novel method to convert approximately Bayesian incentive compatible mechanisms into exactly BIC mechanisms, preserving social welfare and incurring only negligible revenue loss, improving upon previous approaches.

Contribution

The paper presents the first welfare-preserving epsilon-BIC to BIC transformation with negligible revenue loss, using a new type graph approach and applicable to automated mechanism design.

Findings

Transformation preserves social welfare exactly.

Revenue loss is tight and negligible, outperforming previous methods.

Applicable to both Bayesian and ex-post incentive compatible mechanisms.

Abstract

In this paper, we provide a transform from an $\varepsilon$-BIC mechanism into an exactly BIC mechanism without any loss of social welfare and with additive and negligible revenue loss. This is the first $\varepsilon$-BIC to BIC transformation that preserves welfare and provides negligible revenue loss. The revenue loss bound is tight given the requirement to maintain social welfare. Previous $\varepsilon$-BIC to BIC transformations preserve social welfare but have no revenue guarantee~\citep{BeiHuang11}, or suffer welfare loss while incurring a revenue loss with both a multiplicative and an additive term, e.g.,~\citet{DasWeinberg12, Rubinstein18, Cai19}. The revenue loss achieved by our transformation is incomparable to these earlier approaches and can be significantly less. \newnew{Our approach is different from the previous replica-surrogate matching methods and we directly make use of a directed and weighted type graph (induced by the types' regret), one for each agent. The transformation runs a \emph{fractional rotation step} and a \emph{payment reducing step} iteratively to make the mechanism Bayesian incentive compatible.} We also analyze $\varepsilon$-expected ex-post IC ($\varepsilon$-EEIC) mechanisms~\citep{DuettingFJLLP12}. We provide a welfare-preserving transformation in this setting with the same revenue loss guarantee for uniform type distributions and give an impossibility result for non-uniform distributions. We apply the transform to linear-programming based and machine-learning based methods of automated mechanism design.