In this paper, to exploit the challenges and potential offered by the simultaneous use of non-orthogonal multiple access (NOMA) and orthogonal frequency division multiple access (OFDMA) transmission options in future 5G wireless systems, we aim at the proper modeling and transformation of the uplink power allocation problem. In particular, in this setting, each user has two degrees of freedom in the decision making process, namely its overall transmission power level, and the corresponding power investment to the OFDMA and/or NOMA based transmissions. The resulting multi-variable power allocation problem is treated and solved under three different perspectives, namely: 1) Games in Normal Form and Nash Equilibrium (NE); 2) Optimization techniques targeting system social welfare through a centralized optimal solution; and 3) Games in Satisfaction Form and Efficient Satisfaction Equilibrium (ESE). Based on these approaches, different solutions and stable operation points are identified and their properties are analyzed. An in depth evaluation and comparison of the various obtained outcomes is achieved, via modeling and simulations. The focus is placed on the impact and the interplay of the NOMA specific features, including the potential over-exploitation of the available bandwidth, the fairness in accessing it, and the interference treatment. It is also shown that, using the satisfaction form games for the users to converge to the ESE, provides an efficient and promising user-centric modeling approach to the power allocation problem, as the system adapts to the users’ application needs, while at the same time eliminates a significant amount of interference.