In this paper1, we study the discrete power allocation game for the fast fading multiple-input multiple-output multiple access channel. Each player or transmitter chooses its own transmit power policy from a certain finite set to optimize its individual transmission rate. First, we prove the existence of at least one pure strategy Nash equilibrium. Then, we investigate two learning algorithms that allow the players to converge to either one of the NE states or to the set of correlated equilibria. At last, we compare the performance of the considered discrete game with the continuous game in .