The steady expansion of the number of wireless devices and the ubiquity of the networks give rise to various interesting challenges for the future sixth generation (6G) of wireless communication systems. Particularly, the operators have to handle massive connectivity among Machine Type Devices (MTDs) and increasing demand for eMMB through limited spectrum resources. Non-Orthogonal Multiple Access (NOMA) has been spotlighted as an emerging technology to meet the above-mentioned challenges. In this paper, we consider a densely deployed network in which users are divided into NOMA coalitions. Firstly, we model the power allocation problem as a differential game. Then, we extend the formulated game using a Mean Field Game (MFG) theoretic framework by considering the effect of the collective behavior of devices. Furthermore, we derive a distributed power control algorithm that enables the users to appropriately regulate their transmit power according to brief information received from the BS. Indeed, the analysis of the proposed approach is governed by the two fundamental Hamilton- Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations. Numerical results are presented to analyze the equilibrium behaviors of the proposed power control algorithm and to demonstrate the effectiveness of the formulated MFG compared to existing works in the literature.