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We address the adaptive allocation of subcarrier, bit and power resources among the base stations (BSs) of a downlink multi-cell OFDMA system using the non-cooperative game theoretic approach. Unlike the information theoretic approach where continuous bit-loading is used, our algorithm allocates integer number of bits to each subcarrier. Using a utility function with linear pricing on both the transmit bit rate and power, we first show that for a simple two-cell system with single user and fixed modulation, a Nash equilibrium (NE) solution always exists. However, for games formulated on more complicated systems such as with more than two cells, with more than one user in a cell, or when adaptive modulation is used, we observed that the existence of NE cannot be guaranteed. If NE points exist, the game can be played repeatedly with each BS (the player) selects its best strategy until the solution converges, or known as the myopic game. Based on the framework of potential games with coupled constraints, we propose an algorithm which can achieve a stable solution among the players despite that NE solution to the originally problem does not necessarily exist. The convergence of the proposed algorithm is verified by simulation.