This paper considers the minimization of transmit power in Gaussian frequency - selective interference channels, subject to a rate constraint for each user. To derive decentralized solutions that do not require any cooperation among the users, we formulate this power control problem as a (generalized) Nash equilibrium game. We obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem. Then, to compute the solutions of the game, we propose two distributed algorithms based on the single user water¯lling solution: The sequential and the simultaneous iterative water¯lling algorithms, wherein the users update their own strategies sequentially and simultaneously, respectively. We derive a unified set of sufficient conditions that guarantee the uniqueness of the solution and global convergence of both algorithms. Our results are applicable to all practical distributed multipoint-to-multipoint systems, either wired or wireless, where a quality of service in terms of information rate must be guaranteed for each link.