Direction Vector-Based Algorithm for the Nash Bargaining Solution in Dynamic Networks

It is essential for multiuser networks to determine how to efficiently and fairly allocate shared and limited resources. Moreover, it is critical to optimally allocate these resources while ensuring quality of service requirements for users who require tolerable levels of quality. In this letter, we adopt a game-theoretic approach, referred to as the Nash bargaining solution (NBS), for resource allocation across multiple users. While the NBS can provide a fair and optimal resource allocation, finding the NBS is generally a computationally-intensive task, which becomes even more difficult in dynamic networks. We propose a direction vector-based approach that finds accurate solutions to a bargaining problem with relatively low and consistent complexity requirements. The proposed approach exploits the relationship between the direction vectors of utility functions of each user and is used to reduce the search space of the feasible utility set. The simulation results confirm that the proposed approach can efficiently compute the NBS even for a considerable number of users and resources with better accuracy.