Bayesian Mechanism Design with Efficiency, Privacy, and Approximate Truthfulness

TL;DR

This paper explores Bayesian mechanism design integrating differential privacy and approximate truthfulness, achieving optimal efficiency without payments and extending to actual truthfulness under certain models.

Contribution

It introduces Bayesian differential privacy and persistent approximate truthfulness, providing mechanisms that are both private and approximately truthful in the Bayesian setting.

Findings

Mechanisms achieve Bayesian differential privacy and persistent approximate truthfulness.

These mechanisms attain optimal economic efficiency without payments.

Under a modified model, mechanisms can achieve actual truthfulness.

Abstract

Recently, there has been a number of papers relating mechanism design and privacy (e.g., see \cite{MT07,Xia11,CCKMV11,NST12,NOS12,HK12}). All of these papers consider a worst-case setting where there is no probabilistic information about the players' types. In this paper, we investigate mechanism design and privacy in the \emph{Bayesian} setting, where the players' types are drawn from some common distribution. We adapt the notion of \emph{differential privacy} to the Bayesian mechanism design setting, obtaining \emph{Bayesian differential privacy}. We also define a robust notion of approximate truthfulness for Bayesian mechanisms, which we call \emph{persistent approximate truthfulness}. We give several classes of mechanisms (e.g., social welfare mechanisms and histogram mechanisms) that achieve both Bayesian differential privacy and persistent approximate truthfulness. These classes of mechanisms can achieve optimal (economic) efficiency, and do not use any payments. We also demonstrate that by considering the above mechanisms in a modified mechanism design model, the above mechanisms can achieve actual truthfulness.