Given the proven benefits cell densification brings in terms of capacity and coverage, it is certain that 5G networks will be even more heterogeneous and dense. However, as smaller cells are introduced in the network, interference will inevitably become a serious problem as they are expected to share the same radio resources. Another central feature envisioned for future cellular networks is carrier aggregation (CA), which allows users to simultaneously use several component carriers of various widths and frequency bands. By exploiting the diversity of the different carriers, CA can also be used to effectively mitigate the interference in the network. In this paper, we leverage the above key features of next-generation cellular networks and formulate a downlink power setting problem for the different available carriers. Using game theory, we design a distributed algorithm that lets cells dynamically adjust different transmit powers for the different carriers. The proposed solution greatly improves network performance by reducing interference and power consumption, while ensuring coverage for as many users as possible. We compare our scheme to other interference mitigation techniques, in a realistic largescale scenario. Numerical results show that our solution outperforms the existing schemes in terms of user throughput, energy and spectral efficiency.