Efficient and fast resource allocation has become important as the multimedia applications are deployed over multi-user and resource constrained networks. In order to ensure the Quality of Service (QoS) and the collaboration among users resource management strategies based on the cooperative game theory have been proposed. Specifically, we deploy the Nash bargaining solution (NBS) for fair and optimal resource allocation while explicitly considering delay constraints, minimum quality and multimedia characteristics of each user. Moreover, we consider a time-varying channel condition where a fast resource allocation is essential for ensuring QoS. In order to reduce the computational complexity required to find the NBS, we propose a low complexity algorithm based on a transformation that exploits the relationship between feasible utility sets adjacent over time. We show that the complexity required to find the NBS based on the proposed algorithm can be significantly reduced with improved accuracy.