  We study the game theoretic p-Laplacian for semi-supervised learning on
graphs, and show that it is well-posed in the limit of finite labeled data and
infinite unlabeled data. In particular, we show that the continuum limit of
graph-based semi-supervised learning with the game theoretic p-Laplacian is a
weighted version of the continuous p-Laplace equation. We also prove that
solutions to the graph p-Laplace equation are approximately Holder continuous
with high probability. Our proof uses the viscosity solution machinery and the
maximum principle on a graph.
