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Imitation and innovation are the most common ways for people to learn and evolve. However, the combination of imitation and innovation not only inhibits the emergence of cooperation, but also leads to the fragmentation of cooperative clusters. In reality, cooperation exists widely in people's lives. This paper examines how cooperation is maintained in human interaction and what mechanism can eliminate the inhibition of heterogeneous strategy updating rules. To that end, we introduce a reputation mechanism into the traditional prisoner's dilemma model. In our version, the player's reputation is adapted dynamically, and fitness is determined by reputations and strategies. In addition, the players' strategy updating rules are divided into imitation and innovation. The results show that: under the heterogeneous strategy updating rules, the introduction of reputation is beneficial to the emergence of cooperation. Good reputation also enhances the capacity of cooperators to resist temptation. Our research provides insight into the role of reputation under heterogeneous strategy updating rules. • Reputation can eliminate the deterioration of cooperation caused by heterogeneity updating rules. • Good reputations can enhance the capacity of cooperators in both heterogeneity and homogeneity updating rules. • When the influence of reputation is small, innovation players will worsen the survival environment of cooperators. • Innovation players play a significant role in the emergence of cooperation. [ABSTRACT FROM AUTHOR]