Aerial access networks have been envisioned as a promising 6 G technology to enhance the service experience in underserved areas where terrestrial base stations do not exist. In such scenarios, a hierarchical model of high-altitude platforms (HAPs) and unmanned aerial vehicles (UAVs) is considered to provide aerial computing services for ground Internet of Things (IoT) devices. In this study, we investigate a hierarchical aerial computing system to optimally orchestrate the limited computation resources in both HAPs and UAVs. For offloading services, we formulate a joint resource allocation problem to maximize service satisfaction for terrestrial IoT devices. To solve this problem, we employ the ideas of game theory with centralized decision and decentralized execution. Through the Stackelberg-evolutionary game model, the HAP works as a leader, and selects its price strategy based on the evolutionary learning process. As followers, individual UAVs make decisions to partially offload their computing tasks by considering different objectives. According to the interactive control paradigm, our proposed method can get reciprocal advantages for HAPs, UAVs, and ground IoT devices while adaptively handling dynamic aerial network conditions. Finally, extensive simulation results verify the efficiency of our proposed algorithm to increase the usability of edge servers’ computational resources. Compared with other existing state-of-the-art aerial network offloading protocols, we can improve the profits of system throughput, resource usability and UAV fairness up to 10 %, 10 %, and 15 %, respectively.