The steady expansion of the nombre of wireless devices and the ubiquity of the networks give rise to various interesting challenges for the future generation of wireless communication systems. Particularly, the operators have 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 address the above-mentioned challenges. In this paper, we consider a NOMA scenario in which the users are divided into orthogonal coalitions, where each coalition users are served through the same time-code-frequency resource and separated using power levels. Specifically, we address the very dense scenario, where the complexity of centralized solutions become intractable. Firstly, we model the power allocation problem as a differential game. Then, we extend the formulated game to a Mean Field Game (MFG) theoretic framework taking the effect of the collective behavior of devices into consideration. Furthermore, we derive a distributed power control algorithm that enables the users to appropriately regulate their transmit power according to a brief information received from the Base station (BS).