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In this paper, the performance of user fairness of resource allocation is considered in the downlink of relay-based OFDMA cellular systems. In the downlink transparent frame structure, the base stations (BSs) transmit in the first time subslot and the relay stations (RSs) transmit in the second time subslot. A non-cooperative power allocation game is defined for maximizing throughput and reducing co-frequency interference. The distributed process of this game based power allocation scheme is given. Of particular interest in the results is the fairness seen by users and this is compared with equal power allocation, the simulation results showing that the reduced user fairness is worthwhile due to a great power saving.