An efficient use of the radio resources in wireless communications presents a fundamental challenge. While power is one of the most important radio resources, and its control has been studied extensively for voice communications, the increase demand of wireless data service makes it very important to establish power control algorithms for such service. In Code Division Multiple Access (CDMA) cellular systems we have a number of users who are simultaneously sharing the air interface. Each user wants to achieve a high Signal-to-Interference ratio (SIR) at the Base-Station (BS) with the lowest possible transmitted power level. These conflicting objectives of the users make the framework of game theory suitable to establish power control algorithms. In  a non-cooperative power control game (NPG) was proposed where each user unilaterally maximizes his quality of service (QoS), referred to as a ”utility”. The result of such NPG however, is a Nash equilibrium which is not efficient. To obtain a Pareto improvement,  introduced a pricing of the transmit power in which each user’s goal is to maximize a difference between the utility function of NPG and a linear pricing function with respect to the transmit power. However, in  the channel model is not realistic, as they only considered deterministic channel path gains from the BS to the user. Signals in a wireless communications experience different types of fading. In this paper we consider the problem studied in  with three cases of fading: Rayleigh flat fading, Rician flat fading and Nakagami flat fading. In all cases, the channel is assumed to be quasi static, i.e, the fading coefficient is constant during each packet’s duration.
Abdallah, Chaouki T. and M. Hayajneh. "Performance of Game Theoretic Power Control Algorithms for Wireless Data in Fading Channels." (2012). https://digitalrepository.unm.edu/ece_fsp/96