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How to effectively maintain costly intra-group cooperation has always been a topic of great concern in society. As we all know, inter-group competition is a constructive way to promote intra-group cooperation. Previous inter-group competition mechanisms are primarily based on the total contribution value of all individuals in the group in the current round, which ignore the historical behavior of the group and its members. For comparison, we argue that the introduction of collective reputation which reflects not only the total contribution of the groups in the current round but also the group's historical behavior is necessary for the construction of an inter-group competition model. Furthermore, an excellent collective reputation can help the group obtain more high-quality resources and help the group stand out from the competition. To this end, we introduce a new mechanism of inter-group transfer payment driven by collective reputation and construct a public goods game (PGG) model of inter-group competition to study the dynamic behavior of intra-group cooperation evolution. Two parameters, the proportion of accepted groups a and the proportion of transferred groups b , are introduced. The simulation results suggest that the effectiveness of this model in promoting cooperation depends largely on the joint settings of a and b. And in most cases, the combination of small a and medium b plays the significant role. [ABSTRACT FROM AUTHOR]