In this paper, we consider the multiple input multiple output (MIMO) quasi static channel. Our objective is to study the power allocation (over the transmit antennas) problem where not only the performance with respect to (w.r.t.) the transmission reliability but also the cost in terms of the consumed power is accounted for. We first review the existing results w.r.t energy efficiency functions (benefit per cost) which focus mainly on the single input single output (SISO) case and then propose several extensions to the MIMO case. Then, we introduce a new energy efficiency metric based on the outage probability. We conjecture that there is a non-trivial solution to the proposed optimization problem. Several special cases are thoroughly analized and simulation results will be provided to sustain the conducted analysis.