In this work, we propose a new Dual Min-Max Games (DMMG) based self-supervised skeleton action recognition method by augmenting unlabeled data in a contrastive learning framework. Our DMMG consists of a viewpoint variation min-max game and an edge perturbation min-max game. These two min-max games adopt an adversarial paradigm to perform data augmentation on the skeleton sequences and graph-structured body joints, respectively. Our viewpoint variation min-max game focuses on constructing various hard contrastive pairs by generating skeleton sequences from various viewpoints. These hard contrastive pairs help our model learn representative action features, thus facilitating model transfer to downstream tasks. Moreover, our edge perturbation min-max game specializes in building diverse hard contrastive samples through perturbing connectivity strength among graph-based body joints. The connectivity-strength varying contrastive pairs enable the model to capture minimal sufficient information of different actions, such as representative gestures for an action while preventing the model from overfitting. By fully exploiting the proposed DMMG, we can generate sufficient challenging contrastive pairs and thus achieve discriminative action feature representations from unlabeled skeleton data in a self-supervised manner. Extensive experiments demonstrate that our method achieves superior results under various evaluation protocols on widely-used NTU-RGB+D, NTU120-RGB+D and PKU-MMD datasets.