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In this work, we use game theory to analyze the spectrum allocation problem of cognitive radio networks. To deal with the multi Nash equilibrium problem of non-cooperative game based spectrum sharing in cognitive radio networks, we use the variation of utility of cognitive users to judge the stability after several iterations, and design an improved non-cooperative spectrum allocation algorithm. Simulation results shows that the improved non-cooperative spectrum allocation algorithm can achieve stable convergence at the expense of certain degradation of system utility. It is applicable to dealing with the spectrum allocation problem in distributed cognitive radio networks.