Non-orthogonal multiple access (NOMA) is a Fifth Generation (5G) technique that allows many users to simultaneously access the same time–frequency separating channels via successive interference cancellation (SIC) receiver. Cooperative NOMA (CNOMA) is an effective tool to prevent performance degradation of far users by allocating minimal power to users with good channel conditions. In this paper, we proposed a fair power and channel allocation scheme based on the Nash bargaining solution (NBS) game solution in full-duplex, cooperative beamforming (BF) for multicarrier (MC) NOMA. The proposed NBS scheme assigns optimal power and channel allocation according to channel conditions while maintaining a fair rate amongst cooperative users. NBS provides a fair and optimum approach for maximizing the total rate of CNOMA. The signal-to-leakage (SLR) ratio precoding technique is considered as a design performance criterion for beamforming vector towards achieving power domain CNOMA players. Simulation results show that at BER = \({10}^{-5}\), the NBS power allocation (proposed scheme) improved by 2 dB in terms of Signal-to-Noise Ratio (SNR)\(\), compared with the non-cooperative scheme, and 3 dB compared with the multiple-input multiple-output NOMA (MIMO-NOMA). In terms of fairness, the proposed NBS scheme shown a high level of fairness at 0.8401, compared to the other similar approaches in the literature.