The game theory framework in cognitive radio (CR) networks enables the secondary users (SUs) to identify and assign channels left unused by the primary users. The SUs in the network are the players in the game who try to maximize their rate by efficiently allocating power to available sub-channels. The optimal power uses the well-known waterfilling solution until the Nash Equilibrium (NE) is reached. However, the traditionally considered game that maximizes the post-equilibrium sum rate does not consider the time spent in achieving the Nash equilibrium. All water-filling algorithms are a solution to this game, irrespective of the time taken to reach the Nash equilibrium. In this paper, we propose a new game that maximizes effective throughput. So, algorithms that achieve equilibrium faster have higher effective throughput. We present a heuristic solution that uses a fast closed-form water-filling solution known to reduce the computations in each iteration of the NE game. As more time is available for communication, this approach increases the effective sum rate of the CR system by 40% of the achievable sum rate in a typical implementation using LTE parameters. A closed-form solution of the NE of this new game needs further analysis. © 2022 IEEE.