  Incentive mechanism plays a critical role in privacy-aware crowdsensing. Most
previous studies on co-design of incentive mechanism and privacy preservation
assume a trustworthy fusion center (FC). Very recent work has taken steps to
relax the assumption on trustworthy FC and allows participatory users (PUs) to
add well calibrated noise to their raw sensing data before reporting them,
whereas the focus is on the equilibrium behavior of data subjects with binary
data. Making a paradigm shift, this paper aim to quantify the privacy
compensation for continuous data sensing while allowing FC to directly control
PUs. There are two conflicting objectives in such scenario: FC desires better
quality data in order to achieve higher aggregation accuracy whereas PUs prefer
adding larger noise for higher privacy-preserving levels (PPLs). To achieve a
good balance therein, we design an efficient incentive mechanism to REconcile
FC's Aggregation accuracy and individual PU's data Privacy (REAP).
Specifically, we adopt the celebrated notion of differential privacy to measure
PUs' PPLs and quantify their impacts on FC's aggregation accuracy. Then,
appealing to Contract Theory, we design an incentive mechanism to maximize FC's
aggregation accuracy under a given budget. The proposed incentive mechanism
offers different contracts to PUs with different privacy preferences, by which
FC can directly control PUs. It can further overcome the information asymmetry,
i.e., the FC typically does not know each PU's precise privacy preference. We
derive closed-form solutions for the optimal contracts in both complete
information and incomplete information scenarios. Further, the results are
generalized to the continuous case where PUs' privacy preferences take values
in a continuous domain. Extensive simulations are provided to validate the
feasibility and advantages of our proposed incentive mechanism.
