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Dynamic Spectrum Access provides novel solutions to improve spectral efficiency. Wireless Service Providers (WSPs) are allowed to transmit data over their exclusive licensed bands and multiple available unlicensed bands. The critical challenge is how to allocate power rationally to prevent severe interference between coexistent users. We formulate the problem as a Users Coexistence Game (UCG) and verify that it possesses at least one pure-strategy Nash Equilibrium (NE). WSPs play UCGs by an asynchronous-move strategy updating method. Each user determines its own start time and updating period according to the interference. We prove that the method is sure to converge to a unique NE under linear conditions. Finally, simulations are conducted to compare the asynchronous method with the rotational and simultaneous methods. The results show that the asynchronous method can adapt to the interference better and has a more excellent convergence performance.