Inducing Approximately Optimal Flow Using Truthful Mediators

TL;DR

This paper presents a mechanism design approach using differential privacy to induce truthful reporting and nearly optimal flow in network congestion games with unknown demands, without requiring prior distributions.

Contribution

It introduces a weak mediator that ensures truthful reporting and near-optimal flow in network games, even under incomplete information and without prior distributions.

Findings

Mediator achieves asymptotic ex-post Nash equilibrium with truthful reporting.

Players follow suggestions leading to nearly optimal flow.

Develops new private convex programming techniques.

Abstract

We revisit a classic coordination problem from the perspective of mechanism design: how can we coordinate a social welfare maximizing flow in a network congestion game with selfish players? The classical approach, which computes tolls as a function of known demands, fails when the demands are unknown to the mechanism designer, and naively eliciting them does not necessarily yield a truthful mechanism. Instead, we introduce a weak mediator that can provide suggested routes to players and set tolls as a function of reported demands. However, players can choose to ignore or misreport their type to this mediator. Using techniques from differential privacy, we show how to design a weak mediator such that it is an asymptotic ex-post Nash equilibrium for all players to truthfully report their types to the mediator and faithfully follow its suggestion, and that when they do, they end up playing a nearly optimal flow. Notably, our solution works in settings of incomplete information even in the absence of a prior distribution on player types. Along the way, we develop new techniques for privately solving convex programs which may be of independent interest.