Due to the extensive use of unmanned aerial vehicles (UAVs) in civil and military environment, effective deployment and scheduling of a swarm of UAVs are rising to be a challenging issue in edge computing. This is especially apparent in the area of Internet of Things (IoT) where massive UAVs are connected for communications. One of the characteristics of IoT is that an operator can interact with more than one UAVs for the effective scheduling under multi-task requests. Based on this scenario, we clarify the issue on how to maintain the energy efficiency of UAVs and guarantee the reputation gain during the scheduling deployment. In this paper, we first formulate the energy consumption and reputation into the decision model of UAVs scheduling. A game-theoretic scheme is then developed for the optimal decision searching. With the developed model, a range of important parameters of UAV scheduling are thoroughly investigated. Our numerical results show that the proposed scheduling strategy is able to increase the reputation and decrease the energy consumption of UAVs simultaneously. In addition, in the game process, the profit of an operator can be maximized and the network economy research can be explored.