As privacy moves to the center of attention in networked systems, and the need for trust remains a necessity, an important question arises: How do we reconcile the two seemingly contradicting requirements? In this paper, we show that the notion of data-centric trust can considerably alleviate the tension, although at the cost of pooling contributions from several entities. Hence, assuming an environment of privacy-preserving entities, we provide and analyze a game-theoretic model of the trust-privacy tradeoff. The results prove that the use of incentives allows for building trust while keeping the privacy loss minimal. To illustrate our analysis, we describe how the trust-privacy tradeoff can be optimized for the revocation of misbehaving nodes in an ad hoc network.