  We establish necessary and sufficient conditions for a network configuration
to provide utilities that are both fair and efficient in a well-defined sense.
To cover as many applications as possible with a unified framework, we consider
utilities defined in an axiomatic way, and the constraints imposed on the
feasible network configurations are expressed with a single inequality
involving a monotone norm. In this setting, we prove that a necessary and
sufficient condition to obtain network configurations that are efficient in the
weak Pareto sense is to select configurations attaining equality in the
monotone norm constraint. Furthermore, for a given configuration satisfying
this equality, we characterize a criterion for which the configuration can be
considered fair for the active links. We illustrate potential implications of
the theoretical findings by presenting, for the first time, a simple
parametrization based on power vectors of achievable rate regions in modern
cell-less systems subject to practical impairments.
