Approximately Optimal Mechanism Design via Differential Privacy

TL;DR

This paper introduces a differentially private mechanism for approximate optimal implementation in interdependent value models, achieving near-optimal outcomes without utility transfers and ensuring strategy-proofness when values are private.

Contribution

It presents a novel mechanism combining differential privacy and auxiliary strategies to approximate optimal solutions with incentive compatibility and no utility transfers.

Findings

Mechanism achieves near-optimality within a factor of 1/√n.

Mechanism is strategy-proof when values are private.

Applicable to pricing and facility location models.

Abstract

In this paper we study the implementation challenge in an abstract interdependent values model and an arbitrary objective function. We design a mechanism that allows for approximate optimal implementation of insensitive objective functions in ex-post Nash equilibrium. If, furthermore, values are private then the same mechanism is strategy proof. We cast our results onto two specific models: pricing and facility location. The mechanism we design is optimal up to an additive factor of the order of magnitude of one over the square root of the number of agents and involves no utility transfers. Underlying our mechanism is a lottery between two auxiliary mechanisms: with high probability we actuate a mechanism that reduces players' influence on the choice of the social alternative, while choosing the optimal outcome with high probability. This is where the recent notion of differential privacy is employed. With the complementary probability we actuate a mechanism that is typically far from optimal but is incentive compatible. The joint mechanism inherits the desired properties from both.