A mechanism for releasing information about a statistical database with sensitive data must resolve a trade-off between utility and privacy. Privacy can be rigorously quantified using the framework of differential privacy , which requires that a mechanism's output distribution is nearly the same whether or not a given database row is included or excluded. The goal of this paper is strong and general utility guarantees, subject to differential privacy. We pursue mechanisms that guarantee near-optimal utility to every potential user, independent of its side information (modeled as a prior distribution over query results) and preferences (modeled via a loss function). Our main result is: for each fixed count query and differential privacy level, there is a geometric mechanism @math -- a discrete variant of the simple and well-studied Laplace mechanism -- that is simultaneously expected loss-minimizing for every possible user, subject to the differential privacy constraint. This is an extremely strong utility guarantee: every potential user @math , no matter what its side information and preferences, derives as much utility from @math as from interacting with a differentially private mechanism @math that is optimally tailored to @math .
We study the role that privacy-preserving algorithms, which prevent the leakage of specific information about participants, can play in the design of mechanisms for strategic agents, which must encourage players to honestly report information. Specifically, we show that the recent notion of differential privacv, in addition to its own intrinsic virtue, can ensure that participants have limited effect on the outcome of the mechanism, and as a consequence have limited incentive to lie. More precisely, mechanisms with differential privacy are approximate dominant strategy under arbitrary player utility functions, are automatically resilient to coalitions, and easily allow repeatability. We study several special cases of the unlimited supply auction problem, providing new results for digital goods auctions, attribute auctions, and auctions with arbitrary structural constraints on the prices. As an important prelude to developing a privacy-preserving auction mechanism, we introduce and study a generalization of previous privacy work that accommodates the high sensitivity of the auction setting, where a single participant may dramatically alter the optimal fixed price, and a slight change in the offered price may take the revenue from optimal to zero.