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Recently, many self-supervised pre-training methods have been proposed to improve the performance of deep neural networks (DNNs) for 3D point clouds processing. However, the common mechanism underlying the effectiveness of different pre-training methods remains unclear. In this paper, we use game-theoretic interactions as a unified approach to explore the common mechanism of pre-training methods. Specifically, we decompose the output score of a DNN into the sum of numerous effects of interactions, with each interaction representing a distinct 3D substructure of the input point cloud. Based on the decomposed interactions, we draw the following conclusions. (1) The common mechanism across different pre-training methods is that they enhance the strength of high-order interactions encoded by DNNs, which represent complex and global 3D structures, while reducing the strength of low-order interactions, which represent simple and local 3D structures. (2) Sufficient pre-training and adequate fine-tuning data for downstream tasks further reinforce the mechanism described above. (3) Pre-training methods carry a potential risk of reducing the transferability of features encoded by DNNs. Inspired by the observed common mechanism, we propose a new method to directly enhance the strength of high-order interactions and reduce the strength of low-order interactions encoded by DNNs, improving performance without the need for pre-training on large-scale datasets. Experiments show that our method achieves performance comparable to traditional pre-training methods.