Truthful Mechanisms for Agents that Value Privacy

TL;DR

This paper introduces a new model for incorporating privacy into players' utility functions in economic mechanisms, ensuring truthfulness and near-optimal social welfare as the number of players grows.

Contribution

It proposes a novel way to model privacy costs within utility functions, enabling the design of truthful mechanisms that account for privacy in various social choice settings.

Findings

Mechanisms are truthful under the new privacy utility model.

Social welfare approaches optimal levels as the number of players increases.

Applicable to elections, facility location, and general social choice problems.

Abstract

Recent work has constructed economic mechanisms that are both truthful and differentially private. In these mechanisms, privacy is treated separately from the truthfulness; it is not incorporated in players' utility functions (and doing so has been shown to lead to non-truthfulness in some cases). In this work, we propose a new, general way of modelling privacy in players' utility functions. Specifically, we only assume that if an outcome $o$ has the property that any report of player $i$ would have led to $o$ with approximately the same probability, then $o$ has small privacy cost to player $i$. We give three mechanisms that are truthful with respect to our modelling of privacy: for an election between two candidates, for a discrete version of the facility location problem, and for a general social choice problem with discrete utilities (via a VCG-like mechanism). As the number $n$ of players increases, the social welfare achieved by our mechanisms approaches optimal (as a fraction of $n$).