Robust Mediators in Large Games

TL;DR

This paper demonstrates that in large games with private types, strong mediators can implement approximate equilibria of complete-information games, with weak mediators sufficing for congestion games, using joint differential privacy.

Contribution

The paper introduces a novel application of joint differential privacy to implement approximate equilibria via mediators in large games, distinguishing between strong and weak mediators.

Findings

Strong mediators can implement approximate equilibria in large games.

Weak mediators suffice for congestion games.

Differential privacy enables robust mediator design.

Abstract

A mediator is a mechanism that can only suggest actions to players, as a function of all agents' reported types, in a given game of incomplete information. We study what is achievable by two kinds of mediators, "strong" and "weak." Players can choose to opt-out of using a strong mediator but cannot misrepresent their type if they opt-in. Such a mediator is "strong" because we can view it as having the ability to verify player types. Weak mediators lack this ability--- players are free to misrepresent their type to a weak mediator. We show a striking result---in a prior-free setting, assuming only that the game is large and players have private types, strong mediators can implement approximate equilibria of the complete-information game. If the game is a congestion game, then the same result holds using only weak mediators. Our result follows from a novel application of differential privacy, in particular, a variant we propose called joint differential privacy.