Robust Mediators in Large Games∗
Michael Kearns, Mallesh M. Pai, Ryan Rogers, Aaron Roth, and Jonathan Ullman
December 14, 2015
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.