The WoLF-MFGA Algorithm for Equilibrium Analyses of Multiuser Power Control in Wireless Network

Abstract

The main goal of this paper is to explore strategic decision-making of multiuser power control in wireless network from the perspective of mean field game theory. First, we formulate the multiuser power control problem as a $n$ -person noncooperative game and prove the existence of Nash equilibrium for multiuser power control game. Then, we design a new mean field gradient ascent with win or learn fast (WoLF-MFGA) algorithm by introducing mean field term into gradient ascent with the WoLF criterion algorithm. Subsequently, we investigate a sufficient condition of convergence for the proposed WoLF-MFGA algorithm. Furthermore, the WoLF-MFGA algorithm is used to achieve the Nash equilibrium of multiuser power control game, and some simulation results are given. Finally, for the sake of analyzing the convergence of the proposed algorithm, we investigate the sensitivity results of the WoLF-MFGA algorithm.