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We address the problem of downlink beamforming for mitigating the co-channel interference in multi-cell OFDMA networks. Based on the network utility maximization framework, we formulate the problem as a non-convex optimization problem subject to the per-cell power constraints, in which a general utility function of SINR is used to characterize the network performance. To solve the problem in a distributed fashion, we devise an algorithm based on the non-cooperative game with pricing mechanism. We give a sufficient condition for the convergence of the algorithm to the Nash equilibrium (NE). Moreover, to speed up the optimization of the beam-vectors at each cell, we derive an efficient algorithm to solve the KKT conditions at each cell. We provide extensive simulation results to demonstrate that the proposed distributed multi-cell beamforming algorithm converges to an NE point in just a few iterations with low information exchange overhead. Moreover, it provides significant performance gains, especially under the strong interference scenario, in comparison with several existing multi-cell interference mitigation schemes, such as the distributed interference alignment method.