The task scheduling work in the current mobile edge computing (MEC) environment often ignores the dependency between tasks, resulting in a long delay in completion. In response to this problem, first of all, with the goal of reducing the system completion delay, in the multi-user and multi-edge server scenario that takes cross-server collaboration into account, the breadth first search algorithm (BFS) is used to build a dependent task scheduling model. Then, according to the interaction between tasks and edge servers, the joint offloading and migration problem of each scheduling layer in the model are modeled as a Stackelberg game with multiple leaders and multiple followers. Finally, in order to achieve Stackelberg equilibrium, an offloading algorithm based on the Q value and a distributed iterative migration algorithm are proposed to solve the model. The simulation results show that compared with the baseline algorithms, the proposed algorithm reduces the system completion delay by 44. 1% and 63. 2% respectively in the scenarios of users and edge servers with different scales. Further experiments show that compared with the traditional solutions, the proposed model reduces the system completion delay by 20. 1% and 6. 7% respectively in the scenarios of users and edge servers with different scales, and effectively guarantees the quality of service.