With the exponentially increasing number of mobile devices, crowdsensing has been a hot topic to use the available resource of neighbor mobile devices to perform sensing tasks cooperatively. However, there still remain three main obstacles to be solved in the practical system. First, since mobile devices are selfish and rational, it is natural to provide cooperation for sensing with a reasonable payment. Meanwhile, due to the arrival and departure of sensing tasks, resource should be allocated and released dynamically when sensing task comes or leaves. To this end, this paper designs a game theoretic approach based incentive mechanism to encourage the “best” neighbor mobile devices to share their own resource for sensing. Next, in order to adjust resource among mobile devices for the better crowdsensing response, an auction based task migration algorithm is proposed, which can guarantee the truthfulness of announced price of auctioneer, individual rationality, profitability, and computational efficiency. Moreover, taking into account the random movement of mobile devices resulting in the stochastic connection, we also use multi-stage stochastic decision to take posterior resource allocation to compensate for inaccurate prediction. The numerical results show the effectiveness and improvement of the proposed multi-stage stochastic programming based distributed game theoretic methodology (SPG) for crowdsensing.