For multi-user transmissions over MIMO interference channels, each user designs the transmit covariance matrix to maximize its information rate. When passive radio-frequency (RF) energy harvesters are present in the network, the transmissions are constrained by both the transmit power limits and the energy harvesting requirements. A passive RF energy harvester collects the radiated energy from nearby wireless information transmitters instead of using a dedicated wireless power source. It needs multiple transmitters to concentrate their RF radiation on it because typical electric field strengths are weak. In this paper, strategic games are proposed for the multi-user transmissions. First, in a non-cooperative game, each transmitter has a best-response strategy for the transmit covariance matrix that follows a multi-level water-filling solution. A pure-strategy Nash equilibrium exists. Secondly, in a cooperative game, there is no need to estimate the proportion of the harvested energy from each transmitter. Rather, the transmitters bargain over the unit-reward of the energy contribution. An approximation of the information rate is used in constructing the individual utility such that the problem of network utility maximization can be decomposed and the bargaining process can be implemented distributively. The bargaining solution gives a point of rates that is superior to the Nash equilibria and close to the Pareto front. Simulation results verify the algorithms that provide good communication performance while satisfying the RF energy-harvesting requirements.