Nonorthogonal multiple access (NOMA) is viewed as one of the key enabling candidate for the fifth‐generation systems. The effectiveness of such networks heavily relies on the power allocation. This paper addresses the problem of power allocation in a downlink multiuser hybrid NOMA‐orthogonal multiple access (OMA) network, where NOMA is integrated into OMA. Users with strong channel conditions are paired up with the users having weak channel conditions based on a random mechanism. Further, user pairs compete in an auction game for the transmit power being sold by the base station. Bids are placed iteratively by each user pair such that it maximizes their own utility. The existence of a unique Nash equilibrium has been proved theoretically. Simulation results show that the proposed scheme achieves higher average sum rate of users in comparison with that of the existing algorithms.