Posted pricing for robust crowdsensing

Mobile crowdsensing has been considered as a promising approach for large scale urban data collection, but has also posed new challenging problems such as incentivization and quality control. Among the other incentivization approaches, posted pricing has been widely adopted by commercial systems due to the reason that it naturally achieves truthfulness and fairness and is easy to be implemented. However, the fundamental problem of how to set a right posted price in crowdsensing systems remains largely open. In this paper, we study a quality-aware Bayesian pricing problem for mobile crowdsensing where the users' sensing costs and qualities for participating in crowdsensing are drawn from known distributions learned from historical information, and our goal is to choose an appropriate posted price to recruit a group of participants with reasonable sensing qualities for robust crowdsensing, while the total expected payment is minimized. We show that our problem is NP-hard and has close ties with the well known Poisson Binomial Distributions (PBD). To solve our problem, we first discover some non-trivial submodular properties of PBD, which have not been reported before, then we propose a novel "ironing method" that transforms our problem from a non-submodular optimization problem into a submodular one by leveraging the newly discovered properties of PBD. Finally, with the ironing method, an approximate algorithm with provable performance ratio is provided, and we also conduct extensive numerical simulations to demonstrate the effectiveness of our approach.