For over a decade, the Nash bargaining solution (NBS) concept from cooperative game theory has been used in networks as a concept that allows one to share resources fairly. Due to its many appealing properties, it has recently been used for assigning bandwidth in a general topology network between applications that have linear utilities. In this paper, we use this concept for the bandwidth allocation between applications with general concave utilities. We study the impact of concavity on the allocation and present computational methods for obtaining fair allocations in a general topology, based on a dual Lagrangian approach and on Semi-Definite Programming.