Abstract: In a typical cognitive wireless network, multiple secondary users compete to rent for the sub-bands in the authorized spectrum of primary users to transfer data. This paper focuses on simultaneously maximizing the payoff of both primary users and secondary users by jointly optimizing transmit powers of secondary users, sub-band allocation of secondary users, and pricing coefficients of primary users. Specifically, based on backwards induction, this paper decomposes the whole game into three sub optimization problems, i.e., power control problem, sub-band allocation problem, and price adjustment problem. These problems are then solved one by one to obtain the sub-game perfect Nash equilibrium of the whole game. Finally, this paper proposes an algorithm to search for Nash equilibrium. Simulation results verify the theoretical deduction results and effectiveness of the proposed algorithm.