Public Safety Networks (PSN) are expected to provide resilient communication paradigms under disaster recovery scenarios. Towards providing an energy efficient solution an UAV-supported multi-level architecture is employed where user equipments (UEs) are grouped together in clusters. Initially, the UEs choose their role (clusterhead (ch) or cluster member) in the network independently and in a distributed fashion, following the theory of Minority Games (MG), while subsequently the member UEs act as stochastic learning automata selecting a clusterhead to be associated with, based on reinforcement learning. Upon completion of the cluster formation, the UAV optimal positioning in an Euclidean 3D space is obtained by treating a maximization problem of the clusterhead's energy availability, being the UEs that play a critical role within the PSN. Lastly, a non-cooperative game-theoretic approach is adopted to determine in a distributed manner the optimal transmission power (unique Nash equilibrium) of each UE. The performance evaluation of the proposed approach is achieved via modeling and simulation and the corresponding numerical results demonstrate its energy efficiency and effectiveness.