Private Equilibrium Release, Large Games, and No-Regret Learning

We give mechanisms in which each of n players in a game is given their component of an (approximate) equilibrium in a way that guarantees differential privacy — that is, the revelation of the equilibrium components does not reveal too much information about the utilities of other players. More precisely, we show how to compute an approximate correlated equilibrium (CE) under the constraint of differential privacy (DP), provided n is large and any player’s action affects any other’s payoff by at most a small amount. Our results draw interesting connections between noisy generalizations of classical convergence results for no-regret learning, and the noisy mechanisms developed for differential privacy. Our results imply the ability to truthfully implement good social-welfare solutions in many games, such as games with small Price of Anarchy, even if the mechanism does not have the ability to enforce outcomes. We give two different mechanisms for DP computation of approximate CE. The first is computationally efficient, but has a suboptimal dependence on the number of actions in the game; the second is computationally inefficient, but allows for games with exponentially many actions. We also give a matching lower bound, showing that our results are tight up to logarithmic factors. ∗We gratefully acknowledge the support of NSF Grant CCF-1101389. We thank Nabil Al-Najjar, Eduardo Azevdeo, Tymofiy Mylovanov, Andy Postlewaite, Al Roth and Tim Roughgarden for helpful comments and discussions. †Department of Computer and Information Science, University of Pennsylvania. Email:mkearns@cis.upenn.edu. ‡Department of Economics, University of Pennsylvania. Email:mallesh@econ.upenn.edu. §Department of Computer and Information Science, University of Pennsylvania. Email:aaroth@cis.upenn.edu. ¶School of Engineering and Applied Sciences, Harvard University. Email:jullman@seas.harvard.edu.