In this article, we propose a joint access selection and bandwidth allocation method for UAV-assisted wireless communication networks. We consider an application scenario where UAVs act as flying base stations to provide wireless services to ground mobile devices. The interactions among UAVs and mobile devices are modeled as a Stackelberg game, where the UAVs are the leaders and the mobile devices are the followers. The bandwidth allocation among UAVs is modeled as a non-cooperative game, and the access selection of mobile devices is based on the evolutionary game theory. We explore the distributed evolutionary game and the synchronous update and asynchronous update's influence on the convergence results. In addition, a Q-learning approach for access selection is also used as a benchmark. We provide theoretical analysis to show the existence and uniqueness of equilibrium under this hierarchical framework. Finally, simulation results verify the performance of the proposed model.