Impact of Social Learning on Privacy-Preserving Data Collection

Abstract

We study a game-theoretic model where a data collector purchases data from users through a payment mechanism. Each user has her personal signal which represents her knowledge about the underlying state the data collector desires to learn. Through social interactions, each user can also learn noisy versions of her friends’ personal signals, which are called ‘group signals’. We develop a Bayesian game theoretic framework to study the impact of social learning on users’ data reporting strategies and devise the payment mechanism for the data collector accordingly. We show that the Bayesian-Nash equilibrium can be in the form of either a symmetric randomized response (SR) strategy or an informative non-disclosive (ND) strategy. Specifically, a generalized majority voting rule is applied by each user to her noisy group signals to determine which strategy to follow. Our findings reveal that both the data collector and the users can benefit from social learning which drives down the privacy costs and helps to improve the state estimation for a given total payment budget. Further, we derive bounds on the minimum total payment required to achieve a given level of state estimation accuracy.