A differential privacy mechanism that accounts for network effects for crowdsourcing systems

In crowdsourcing systems, it is important for the crowdsource campaign initiator to incentivize users to share their data to produce results of the desired computational accuracy. This problem becomes especially challenging when users are concerned about the privacy of their data. To overcome this challenge, existing work often aims to provide users with differential privacy guarantees to incentivize privacy-sensitive users to share their data. However, this work neglects the network effect that a user enjoys greater privacy protection when he aligns his participation behaviour with that of other users. To explore this network effect, we formulate the interaction among users regarding their participation decisions as a population game, because a user's welfare from the interaction depends not only on his own participation decision but also the distribution of others' decisions. We show that the Nash equilibrium of this game consists of a threshold strategy, where all users whose privacy sensitivity is below a certain threshold will participate and the remaining users will not. We characterize the existence and uniqueness of this equilibrium, which depends on the privacy guarantee, the reward provided by the initiator and the population size. Based on this equilibria analysis, we design the PINE (Privacy Incentivization with Network Effects) mechanism and prove that it maximizes the initiator's payoff while providing participating users with a guaranteed degree of privacy protection. Numerical simulations, on both real and synthetic data, show that (i) PINE improves the initiator's expected payoff by up to 75%, compared to state of the art mechanisms that do not consider this effect; (ii) the performance gain by exploiting the network effect is particularly good when the majority of users are flexible over their privacy attitudes and when there are a large number of low quality task performers