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In this paper, we exploit the capabilities of Fully Autonomous Aerial Systems' (FAAS) and the Mobile Edge Computing (MEC) to introduce a novel data offloading framework and support the energy and time efficient video processing in surveillance systems based on game theory in satisfaction form. A surveillance system is introduced consisting of Areas of Interest (AoIs), where a MEC server is associated with each AoI, and a FAAS is flying above the AoIs to collectively support the IP cameras' computing demands. Each IP camera adopts a utility function capturing its Quality of Service (QoS) considering the experienced time and energy overhead to offload and process its data either remotely or locally. A non-cooperative game among the cameras is formulated to determine the amount of offloading data to the MEC server and/or the FAAS. The novel concept of Satisfaction Equilibrium (SE) is introduced where the IP cameras satisfy their minimum QoS prerequisites instead of maximizing their performance by wasting additional system resources. A distributed learning algorithm determines the IP cameras' stable data offloading, while a reinforcement learning algorithm determines the FAAS's movement among the AoIs exploiting the accuracy, timeliness, and certainty of the collected data by the IP cameras per AoI. The performance evaluation of the proposed framework is achieved via modeling and simulation.