This work deals with the power allocation problem in a multipoint-to-multipoint network, which is heterogenous in the sense that each transmit and receiver pair can arbitrarily choose whether to selfishly maximize its own rate or energy efficiency. This is achieved by modeling the transmit and receiver pairs as rational players that engage in a non-cooperative game in which the utility function changes according to each player’s nature. The underlying game is reformulated as a quasi variational inequality (QVI) problem using convex fractional program theory. The equivalence between the QVI and the non- cooperative game provides us with all the mathematical tools to study the uniqueness of its Nash equilibrium (NE) points and to derive novel algorithms that allow the network to converge to these points in an iterative manner both with and without the need for a centralized processing. Numerical results are used to validate the proposed solutions in different operating conditions.