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• Edge dynamics means that each player in the network can use different strategies for four neighbors. • Interactive diversity is one way of selecting policy referees. • Introduce individual reputation and explore how the co-evolution of reputation and strategy affects cooperative behavior. In view of social interactions, people are more inclined to make different decision-making behaviors based on the credibility of different individuals. In this article, based on edge dynamics, that is, players can freely choose different strategies for different opponents, we introduce individual reputation, which is judged by others based on individual performance, thereby exploring how co-evolution of reputation and strategy affects cooperation behavior. A large number of simulation results show that under the condition of diversity interaction, other people's greater decision-making power on individuals' reputation can significantly promote cooperative behavior. It provides scholars with new insights into the social dilemma under the framework of edge dynamic. [ABSTRACT FROM AUTHOR]