well as the CRAN remote radio heads seek to choose their optimal power to maximize their users' rates. The problem is formulated as a noncooperative game in which the players are the CRAN cloud and the BSs. Given the difference of capabilities between the CRAN and the various BSs, the game is cast within the framework of cognitive hierarchy theory. In this framework, players are organized in a hierarchy in such a way that a player can choose its strategy while considering players of only similar or lower hierarchies. Using such a hierarchical design, one can reduce the interference caused by the CRAN and high-powered base stations on low-powered BSs. For this game, we analyze the properties of the Nash equilibrium and the cognitive hierarchy equilibrium. Simulation results show that the proposed cognitive hierarchy model yields significant performance gains, in terms of the total rate, reaching up to twice the rate achieved by a classical noncooperative game's Nash equilibrium.