Fair and efficient subcarrier assignment for an infrastructure-based cellular OFDMA network is a challenging problem due to interferences from neighboring cells. In this paper, we investigate this problem using potential game theory, where the utility function adopted is meant for minimizing the co-channel interferences among different players. Each of these players is considered to be a cell with a central base station (BS) and its multiple mobile stations (MS) in a downlink scenario. Under such formulation, we establish the potential game. Hence, a Nash equilibrium (NE) will be guaranteed for the proposed game, which can be achieved via certain strategy dynamics such as the best/better responses. We propose our iterative algorithm for obtaining the NEs and present numerical results to evaluate the performance of our game. Improvement in efficiency and fairness is observed in this study.