This paper studies the precoding design in a multicell multiuser (MU) system with universal frequency-reuse using a game-based approach. Considered is a multicell system, where the MU downlink transmissions in each cell are facilitated by a multi-antenna base-station (BS). In particular, the BS wishes to maximize the transmission sum-rate to its connected mobile-stations (MS) by the means of zero-forcing (ZF) precoding. In this context, the paper considers a strategic non-cooperative game (SNG), where each BS greedily determines its optimal power allocation in a distributed manner, based on the knowledge of the out-of-cell interference (OCI) at its connected MSs. Via the game theory framework, we study the existence and uniqueness of a Nash equilibrium (NE) of this multicell game. It is shown that a NE of the game always exists, whereas the NE uniqueness is guaranteed under a certain condition on the OCI. Numerical results confirm with the analysis that a small OCI level almost always leads to the NE's uniqueness. Simulations also show that the multicell game using known OCI knowledge provides additional sum-rate gains over the scheme with no OCI information.