This paper presents the deep learning-based recent achievements to resolve the problem of autonomous mobility control and efficient resource management of autonomous vehicles and UAVs, i.e., (i) multi-agent reinforcement learning (MARL), and (ii) neural Myerson auction. Representatively, communication network (CommNet), which is one of the most popular MARL algorithms, is introduced to enable multiple agents to take actions in a distributed manner for their shared goals by training all agents' states and actions in a single neural network. Moreover, the neural Myerson auction guarantees trustfulness among multiple agents as well as achieves the optimal revenue of highly dynamic systems. Therefore, we survey the recent studies on autonomous mobility control based on MARL and neural Myerson auction. Furthermore, we emphasize that integration of MARL and neural Myerson auction is expected to be critical for efficient and trustful autonomous mobility services.