The bounded rationality of agents plays an important role in the performance of complex systems. In this work, we explore the influence of bounded rationality on the evolution of cooperation, defection and extortion strategies on a regular lattice by applying the Fermi dynamics in the Prisoner's Dilemma game. It is found that the rationality level plays a non-trivial role in the emergence of cooperation with extortion in structured systems. On the one hand, for the perfect rationality case, it is difficult for cooperators to resist the invasion of defection. On the other hand, being too irrational breaks the stable structure between cooperators and extortioners, and results in the extinction of cooperation. Hence, there is a proper level of bounded rationality which can slow down the expansion of defective and extortionate behaviors, and promote the emergence of cooperation-extortion alliances, which can yield a better outcome to the whole system. This study may provide some clues to optimize the performance of multi-agent systems with bounded rationality.