Inter-cell interference management is one of the most important issues in next generation wireless networks. In this paper, a transmit power adaptation method using a non cooperative game theory approach is developed in such a way to reduce the inter-cell interference in the whole network. The gaming problem is formulated by allowing that a subchannel could be shared by multiple neighboring cells (i.e. universal frequency reuse). The data rate is enhanced by finding the optimum transmit power for each co-channel user using game theory-based scheme. The performance of the proposed scheme is analyzed and compared with existing scheme. Simulation and analytical results are presented to show the effectiveness of the proposed scheme.