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This paper investigates the subcarrier allocation problem for a downlink multi-cell multiuser OFDMA network using potential game theory. Each player is considered to be a central base station together with all the mobiles distributed within its coverage area. In such a system, co-channel interferences (CCI), if left uncontrolled, could hinder the transmissions and limit the throughputs of the users, especially those near the cell-edge area. Certain remedies, including power control with pricing, did not seem to solve the problem completely. We specifically address this issue from an interference-minimizing approach, where the utility function adopted is meant to minimize the total CCI among players. Under such formulation, we show that the formulated game can be mathematically described by a potential game. Hence, a Nash equilibrium (NE) will be guaranteed for the proposed game and stable solutions can be achieved via myopic gameplays such as the best/better responses. We propose our iterative algorithm for obtaining the NEs and address several performance issues such as fairness for edge-users and the price of anarchy. Numerical results show the improvement in efficiency and fairness using this approach.