Differentially private and incentive compatible recommendation system for the adoption of network goods

We study the problem of designing a recommendation system for network goods under the constraint of differential privacy. Agents living on a graph face the introduction of a new good and undergo two stages of adoption. The first stage consists of private, random adoptions. In the second stage, remaining non-adopters decide whether to adopt with the help of a recommendation system A. The good has network complimentarity, making it socially desirable for A to reveal the adoption status of neighboring agents. The designer's problem, however, is to find the socially optimal A that preserves privacy. We derive feasibility conditions for this problem and characterize the optimal solution.