  In this paper, an energy efficiency (EE) game in a MIMO multiple access
channel (MAC) communication system is considered. The existence and the
uniqueness of the Nash Equilibrium (NE) is affirmed. A bisection search
algorithm is designed to find this unique NE. Despite being sub-optimal for
deploying the $\varepsilon$-approximate NE of the game when the number of
antennas in transmitter is unequal to receiver's, the policy found by the
proposed algorithm is shown to be more efficient than the classical allocation
techniques. Moreover, compared to the general algorithm based on fractional
programming technique, our proposed algorithm is easier to implement.
Simulation shows that even the policy found by proposed algorithm is not the NE
of the game, the deviation w.r.t. to the exact NE is small and the resulted
policy actually Pareto-dominates the unique NE of the game at least for 2-user
situation.
