  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. A small-cell network is
considered as a possible case study of this heterogeneous scenario. Numerical
results are used to validate the proposed solutions in different operating
conditions.
