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.

翻译：我们建立了网络配置在有明确定义下同时实现公平与高效效用的充要条件。为在统一框架下覆盖尽可能多的应用场景，我们采用公理化方式定义效用函数，并通过含单调范数的单一不等式表达可行网络配置的约束条件。在此设定下，我们证明：获得弱帕累托意义上高效网络配置的充要条件是选择满足单调范数等式的配置。进一步地，针对满足该等式的给定配置，我们刻画了一个可判定该配置对活跃链路是否公平的准则。通过首次给出受实际损伤约束的现代去蜂窝系统中可达速率区域基于功率向量的简单参数化表示，我们展示了理论发现的潜在应用价值。