The field of semi-supervised learning involves learning from both labeled and unlabeled data. By exploiting the structure of the unlabeled data, such as its geometric or topological properties, semi-supervised classifiers can obtain good performance with far fewer labels than are required in fully supervised learning (when classifiers learn only from labeled data). A semi-supervised approach is necessary when labels are very expensive to obtain, as is the case in a majority of classification applications, such as website classification, text recognition, protein sequencing, medical imaging, natural language processing. In this talk we apply p-Laplacian regularization to cases of very low labeling rate; in such applications this approach classifies properly when the standard Laplacian regularization does not. Using the two-player stochastic game interpretation of the p-Laplacian, we prove asymptotic consistency of p-Laplacian regularized semi-supervised learning, thus justifying the utility of the p-Laplacian. This is joint work with Jeff Calder.