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The power allocation problem with co-channel interference is studied in multi-cell OFDMA cellular relay systems. The multi-cell non-cooperative power allocation game model is given in the first time subslot for base stations (BSs) and in the second time subslot for relay stations (RSs) respectively. In all the cells, each transmitter (BS or RS) controls the power allocation on each subchannel to maximize its own utility in a distributed way. In the first time subslot, a match factor is defined for considering the mismatch between the first hop link data rate and the second hop link data rate and the pricing factor for the RS will be adjusted adaptively by this match factor. As a Nash equilibrium is used to determine the solution of this problem, the existence and uniqueness of the Nash equilibrium are studied. The simulation results of system throughput and transmission power of BS and RS is given with different pricing factors. Compared with equal power allocation, the system throughput is improved and transmission power is reduced.