The replicator dynamics model is an evolutionary game concept that describes the state of a population in a process inspired by natural selection. This model is used to analyze a resource allocation problem in distributed networked systems. The main properties of the replicator equation are analyzed to propose a novel technique based only on the available information of a system modeled as a connected graph. Likewise, we analyze the stability of the equilibrium points as a function of a certain class of fitness. Finally, an economic dispatch in distributed generation systems is presented in order to illustrate the theoretical results.