Distributed Generalised Nash Equilibrium Seeking and Its Application to Femtocell Networks

In this paper, distributed algorithms are developed to search the generalised Nash equilibrium with global constraints. Relations between the variational inequality and the Nash equilibrium are investigated via the Karush-Kuhn-Tucher (KKT) optimal conditions, which provide the underlying principle for developing the distributed algorithms. Two time-varying consensus schemes are proposed for each agent to estimate the actions of others, by which a distributed framework is established. The algorithm with fixed gains is designed with certain system knowledge, while the adaptive algorithm is proposed to address the problem when the system parameters are not available. The asymptotic convergence to the Nash equilibrium is established through Lyapunov theory and the consensus theory. The power control problem in a femtocell network is formulated as a Nash game, and is solved by the proposed algorithms. Simulation results are provided to verify the effectiveness of the theoretical development.