In this paper, we consider an open-loop network MIMO system with K BSs serving K private MSs and Mc common MS based on a novel partial cooperation overlaying scheme. Exploiting the heterogeneous path gains between the private MSs and the common MSs, each of the K BSs serves a private MS non-cooperatively and the K BSs also serve the Mc common MSs cooperatively. The proposed scheme does not require closed loop instantaneous channel state information feedback, which is highly desirable for high mobility users. Furthermore, we formulate the long-term distributive power allocation problem between the private MSs and the common MSs at each of the K BSs using a partial cooperative game. We show that the long-term power allocation game has a unique Nash Equilibrium (NE) but standard best response update may not always converge to the NE. As a result, we propose a low-complexity distributive long-term power allocation algorithm which only relies on the local long-term channel statistics and has provable convergence property.