Existence of Nash Equilibria in Wireless Networks: An Adaptive Power Control Scheme for Radio Resource Management

Radio resource management (RRM) is one of the most challenging and one of the most important aspects of modern wireless communication networks. Many interactive decision making processes are required to design an intelligent radio resource management scheme that can significantly improve the system performance. These interactive decision making processes of RRM can be well analyzed by the application of game theory. The purpose of this paper is to analyze the power management in cognitive radio Direct Sequence Spread Spectrum (DS-SS) wireless networks from the viewpoint of game theory. The main focus is to model and analyze an adaptive power control scheme in wireless networks using non cooperative game. Our approach is based on a model for the utility that a wireless user or node derives from using the system. Using this model, we show a distributed adaptive power control scheme that maximizes utility of each user of the networks. Formulating this as a game we show the existence and uniqueness of the Nash equilibrium that achieved by the application of game theory.