This study investigates the impact of reputation-based imitation-mutation dynamics on the evolution of cooperation in evolutionary games. The research explores how individual reputation, directly linked to collected payoff, influences strategy updates and cooperation levels in spatial populations with different interaction topologies, including lattices, small-world, and scale-free graphs. The study introduces an extended strategy update rule, combining imitation with random strategy mutation, to account for potential irrational choices in decision-making. The results show that the extended dynamics significantly enhance cooperation levels compared to traditional imitation rules. In particular, the introduction of mutation allows for more stable cooperation, especially in high-temptation scenarios. The study also reveals that the mutation rate and reputation update parameter have complex effects on cooperation levels, with optimal values depending on the dilemma strength. For instance, in the prisoner's dilemma game, higher mutation rates can reduce the effectiveness of the reputation mechanism, while in the snowdrift game, the extended dynamics consistently lead to lower cooperation levels than pure imitation. The study highlights the importance of considering both reputation mechanisms and strategy updates in evolutionary game theory. It demonstrates that the combination of imitation and mutation provides a more efficient strategy update process, leading to better cooperation outcomes. However, the model has limitations, such as the uniform application of mutation rates across all individuals, which could be improved by introducing individual-specific mutation rates. Overall, the research contributes to the understanding of cooperation in complex social systems and provides insights into the role of reputation and irrational decision-making in evolutionary processes.This study investigates the impact of reputation-based imitation-mutation dynamics on the evolution of cooperation in evolutionary games. The research explores how individual reputation, directly linked to collected payoff, influences strategy updates and cooperation levels in spatial populations with different interaction topologies, including lattices, small-world, and scale-free graphs. The study introduces an extended strategy update rule, combining imitation with random strategy mutation, to account for potential irrational choices in decision-making. The results show that the extended dynamics significantly enhance cooperation levels compared to traditional imitation rules. In particular, the introduction of mutation allows for more stable cooperation, especially in high-temptation scenarios. The study also reveals that the mutation rate and reputation update parameter have complex effects on cooperation levels, with optimal values depending on the dilemma strength. For instance, in the prisoner's dilemma game, higher mutation rates can reduce the effectiveness of the reputation mechanism, while in the snowdrift game, the extended dynamics consistently lead to lower cooperation levels than pure imitation. The study highlights the importance of considering both reputation mechanisms and strategy updates in evolutionary game theory. It demonstrates that the combination of imitation and mutation provides a more efficient strategy update process, leading to better cooperation outcomes. However, the model has limitations, such as the uniform application of mutation rates across all individuals, which could be improved by introducing individual-specific mutation rates. Overall, the research contributes to the understanding of cooperation in complex social systems and provides insights into the role of reputation and irrational decision-making in evolutionary processes.