Bridging Central and Local Differential Privacy in Data Acquisition Mechanisms

We study the design of optimal Bayesian data acquisition mechanisms for a platform interested in estimating the mean of a distribution by collecting data from privacy-conscious users. In our setting, users have heterogeneous sensitivities for two types of privacy losses corresponding to local and central differential privacy measures. The local privacy loss is due to the leakage of a user's information when she shares her data with the platform, and the central privacy loss is due to the released estimate by the platform to the public. The users share their data in exchange for a payment (e.g., through monetary transfers or services) that compensates for their privacy losses. The platform does not know the privacy sensitivity of users and must design a mechanism to solicit their preferences and then deliver both local and central privacy guarantees while minimizing the estimation error plus the expected payment to users.