Abstract: In the iterated prisoners’ dilemma game, zero-determinant strategies can unilaterally form a linear relationship between the payoffs of the players, where the extortion strategy always obtains a benefit no less than that of her opponent. We focus on the evolution of the cooperation defection and extortion strategies on the grid network when agents update their strategies by replication-aspiration dynamic. By means of Monte Carlo simulations, we find that the extortion strategy promotes the boost of the cooperation on the grid network under the mixed updating rule. We explain the results by the micro dynamic of the process and find that the existence of "cooperator - extortioner alliance" can help the cooperators resist the invasion of the defectors and the strength of the extortion strategies plays a non-trivial role on the evolution of cooperation.