With the wide adoption of unmanned aerial vehicles (UAVs) in our daily life, using UAVs to collect sensing data from the surrounding environment has become a practice. Notably, people use UAVs to capture videos and upload them to Youtube. Accordingly, using distributed UAVs in the city to collect real-time data represents a key enabling approach for smart city, e.g., air pollution and traffic monitoring. To achieve this goal, in this work, we develop a UAV-based crowdsensing system that allows UAVs to dynamically join and contribute to data collection. We make three contributions. First, due to UAVs' highspeed spatial mobilities, diverse sensing capabilities, and limited energy reserves, it is key to stimulate UAVs to cooperatively perform sensing tasks. To address this issue, we develop a game theory-based distributed UAV incentive scheme, named BASIC. Second, to make BASIC work fully distributed and scalable, we first develop a mathematical model to characterize the interdependent operations of task requesters and collaboratively data sensing. We then devise a centralized auction mechanism with truthful bidding for UAVs. A heuristic algorithm is then devised to select the winning UAVs for sensing tasks and determine the proper payments to winners. Last, we perform extensive simulations to validate the effectiveness and show that BASIC can provide effective incentive as compared to the existing schemes.