Non-orthogonal multiple access (NOMA) has been considered as one of the key enabling techniques for next-generation wireless networks and the overall performance of these systems largely depends on the power allocation (PA). In this Letter, the authors address the PA problem in a downlink cellular NOMA network. They propose an auction-based mechanism in which the users compete for the transmit power being sold by the base station. Each user places his bid iteratively in order to maximise his own utility. Further, the authors prove the existence of an unique Nash equilibrium theoretically. Simulation results demonstrate the effectiveness of the proposed scheme in terms of the average sum rate of users as compared to an existing algorithm.