The rapidly growing demand for vast numbers of Internet of Things (IoT), in both urban and rural areas, necessitates their ceaseless and automatic energy supply. This is particularly vital in cases where the IoT sensors are deployed in inaccessible locations outside of human reach. In this direction, unmanned aerial vehicles (UAVs) with wireless power transfer (WPT) capabilities can solve this issue, due to their flexible deployment. To this end, we devise an architecture in which a UAV swarm covers the energy demand of an IoT network, while at the same time, the UAVs fulfil their energy needs through a charging station (CS) infrastructure. A practical energy model is considered, which takes into account the battery levels of the UAVs, energy consumption due to transition to different locations, hovering, and WPT. Also, to capture the UAV-CS interaction, an economic model is introduced. The UAVs aim to maximize their profit by transferring energy to the IoT, while the CSs aim to maximize their profit by recharging the UAVs. To ensure a profit-wise stable CS-UAV association, while providing energy coverage to the IoT, we formulate a many-to-one matching game. Due to inter-dependencies between UAVs’ utilities, i.e., externalities, a matching algorithm based on peer effects and two- sided exchange-stability is proposed. To further evaluate the con- sidered system, we design an optimization scheme which performs the UAV-CS assignment with the aim to maximize the energy coverage of the IDs. Numerical results showcase the matching algorithm’s ability to provide near-optimal energy coverage to the IDs, while balancing fairness among the competing agents’ profit, compared to the optimization scheme.