Data reporters have privacy concerns when they are requested to contribute personal data to a data collector. Such privacy concerns are strengthened by data correlation and social relationship, as the data correlation could inevitably cause privacy issues to their socially-connected individuals who even do not report the data. However, both factors are hard to quantify precisely in practice due to their private nature. Such an incomplete information situation poses great challenges for the data reporters to determine their coupled privacy-preserving strategies and for the data collector to choose a proper privacy-preserving mechanism. This motivates us to propose a novel Bayesian game-theoretic framework to analyze the data reporters’ behaviors. We show that the game has a symmetric Bayesian Nash Equilibrium (BNE) with a threshold structure, which builds a connection between the data reporter’s action and privacy concern under incomplete information. The complicated relationship between the BNE and the data collector’s strategy makes it difficult to solve the data collector’s optimization problem. However, by exploiting the unimodal feature of the problem, we present a low-complexity algorithm to compute the optimal privacy-preserving mechanism. Through analytical and numerical studies, we find that the lack of complete information could cause the data reporters to adopt more conservative strategies but make the data collector adopt a less conservative mechanism, resulting in an overall privacy protection degradation. The simulations further demonstrate that the degradation could be alleviated by stronger data correlation and social relationship, and a higher probability of serious privacy concerns.