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It has been well recognized that the capacity of a wireless system is usually limited because of intracell interference and intercell interference (ICI), and many technologies have been used to combat against them in different systems. Here, we consider a closed-loop wireless network with a limited feedback rate. In such networks, channel state information (CSI) feedback has become a well recognized technique that significantly increases the down link capacity by suppressing interference. However, the existing work typically focuses more on discussing each individual mobile station (MS) rather than modeling the interactions among self-interested users in the network level. In addition, the ICI is always not considered. To this end, we propose an alternative approach to investigate CSI and ICI simultaneously in one feedback control problem in the analytical setting of a game theoretic framework, in which a multiple-antenna base station (BS) communicates with a number of co-channel MSs through a linear precoder with the co-channel cells around. Specifically, we present a feedback-rate control game using sequential second price auction, in which the feedback rate is divided into homogeneous units and auctioned off sequentially among the MSs, and for each MS the feedback rate is optimized between CSI and ICI in order to gain the largest channel capacity. Our goal is to find a productive and justified mechanism to distribute the total feedback rate, which brings not only a good performance in the sum channel capacity but also a preservation in fairness among the MSs. Simulation results show that the proposed game achieves promising performance in both efficiency and fairness under randomness of terminal location and the time-varying nature of wireless channels.