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In this work, we formulate the potential game model of joint channel selection and power allocation. First, under the interference constraint, a nonlinear optimization problem is formulated for improving the total throughput and considering the fairness in cognitive radio network. we also define the special objective function for each transmitting node and formulate a potential game to solve this problem distributively. The Nash equilibria of this potential game is investigated. It is shown that the distributed sequential play converges to a Nash equilibrium point and quickly satisfy the interference constraint. Finally, through simulations, the performances are examined and we further investigate the relationship between the parameters of the objective function and the performances of the whole cognitive radio network.