In spite of the pronounced benefit brought by crowdsensing, a user would not participate in sensing without adequate incentive, indicating that effective incentive design plays a critical role in making crowdsensing a reality. In this work, we examine the impact of two conflicting factors on incentives for users' participation: 1) the concern about privacy leakage and 2) the (positive) network effect from many sensing participants. The former factor hinders privacy- aware users from participating, whereas the latter encourages users' participation. Taking into consideration both factors, we devise a privacy-preserving crowdsensing scheme, in which a reverse 'privacy' auction is first run by the crowdsensing platform to select users based on their privacy valuations and the network effect. Then the trusted platform carries out differentially private data aggregation over the collected data such that the released sensing result remains useful for the task agent, while all participants' data privacy is guaranteed. A natural objective here is then to maximize the profit of the task agent, i.e., the difference between its utility and the total reward to the participants. To this end, the platform utilizes a random-sampling based mechanism for the 'privacy' auction, followed by a Laplace mechanism for data aggregation. We show that this auction mechanism design is 4-competitive, and further it exhibits desirable properties, including individual rationality, truthfulness, computational efficiency. Simulation results corroborate the theoretical properties of the proposed privacy-preserving crowdsensing scheme.