Aiming at minimizing the computation delay and energy consumption of user equipment (UE) in an unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system, a joint optimization of UAV deployment and UE offloading strategy was proposed based on a game-theoretic approach. Considering the selfish and rational nature of the devices, the UAV-assisted MEC system was modeled as a two-layer Stackelberg game, with the UAVs as the leaders and the UEs as the followers. At the follower layer, an improved coalition formation game was utilized to minimize the total computational cost of the UEs. At the leader layer, the throughput of the UAV was maximized through an exact potential game. The existence of Nash equilibra at the follower and leader layers was proved by using backward induction, and the existence of a Stackelberg equilibrium (SE) for the proposed overall game was further proved. A Stackelberg-based two-layer iterative algorithm was proposed to achieve the SE. Simulation results show that the proposed algorithm significantly outperforms the baseline algorithm while guaranteeing convergence and low complexity.