Aiming at the high complexity of the cognitive relay selection strategy algorithm in cognitive collaborative networks under the interference power constraint from secondary users to the primary receivers, the selfinterference constraint at each secondary relay and the total power constraint for the secondary system, we propose a full duplex relay selection strategy based on potential game. The relay selection problem is modeled as a potential game where the total rate of cognitive collaborative networks is regarded as the common utility function. Then the game model is analyzed. On the premise of the absence of the information of the infeasible strategy sets, we solve the conditions which guarantee the existence and feasibility of the pure Nash Equilibrium (NE) in the proposed game. Furthermore, in order to achieve a pure strategy NE, we propose a cognitive fullduplex relay iterative algorithm, and discuss the complexity of the proposed algorithm. Simulation results show that the proposed algorithm can obtain a performance of optimal or near optimal rate with low complexity, and achieve a significant performance gain compared with the traditional half duplex mode.