An Exchange Market Approach to Mobile Crowdsensing: Pricing, Task Allocation, and Walrasian Equilibrium

Pricing and task allocation are vital to improving the efficiency in mobile crowdsensing, an emerging human-in-the-loop application paradigm. Previous studies focused on incentive mechanism design for specific sensing applications where one party (either task initiators or platform) can dominate the pricing and task allocation process. These results, however, are not applicable to a free crowdsensing market where multiple task initiators and task participants (mobile users), as peers, are engaged to maximize their own interests. New incentive mechanisms are pressingly needed to produce a solution, so that the interests of all participating parties can be considered. In this paper, appealing to exchange economy theory, we employ the notion of 'Walrasian Equilibrium' as a comprehensive metric, at which there exists a price vector for mobile users and an allocation for task initiators such that the allocation is Pareto optimal and the market gets cleared (i.e., all sensing tasks are performed). We consider a standard model where the utility function for sensing quality is monotonically increasing, differentiable, and concave, and the payoff function for a mobile user is linear. To address the problem, we first characterize the supply-demand pattern for a given price vector, which is the subset of mobile users selected by each task initiator to perform the task. We then devise methods for validating the existence of a Walrasian Equilibrium within each supply-demand pattern. One key step is to divide the space of prices into a collection of appropriate cells, based on the hyperplane arrangement, so that each cell has a unique supply-demand pattern. We devise an algorithm that can find a Walrasian Equilibrium in polynomial time, for a case of practical interest where the classes of mobile devices are bounded. Based on the insight, we further consider the general case and design an efficient pattern search (EPS) algorithm to reduce the search space, thus accelerating the search process accordingly. This is realized by choosing the supply-demand pattern which is closer to the 'Walrasian Equilibrium' than the pattern in previous iteration in the search process. Our results show that EPS can find an ∈ -approximation Walrasian Equilibrium in polynomial time for the general case, given a constant ∈.