This study addresses the problem of jointly optimizing the transmit beamformers and power control in multi-user multiple-input multiple-output (MIMO) downlink. The objective is minimizing the total transmission power while satisfying the signal-to-noise plus interference ratio (SINR) requirement of each user. Before power control, it uses the maximum ratio transmission (MRT) scheme to determine the beamformers due to its attractive properties and the simplicity of handling. For power control it introduces a supermodular game approach and proposes an iterated strict dominance elimination algorithm. The algorithm is proved to converge to the Nash equilibrium. Simulation results indicate that this joint optimization method assures the improvement of performance. This objective addresses the problem of jointly optimizing the transmit beamformers and power control in multi-user multiple-input multiple-output (MIMO) downlink. The objective is minimizing the total transmission power while satisfying the signal-to-noise plus interference ratio (SINR Before power control, it uses the maximum ratio transmission (MRT) scheme to determine the beamformers due to its attractive properties and the simplicity of handling. For power control it introduces a supermodular game approach and proposes an iterated strict dominance elimination algorithm. The algorithm is proved to converge to the Nash equilibrium. Simulation results indicates that this joint optimization method assures the improvement of performance.