Graph transduction is a popular class of semi-supervised learning techniques, which aims to estimate a classification function defined over a graph of labeled and unlabeled data points. The general idea is to propagate the provided label information to unlabeled nodes in a consistent way. In contrast to the traditional view, in which the process of label propagation is defined as a graph Laplacian regularization, here we propose a radically different perspective that is based on game-theoretic notions. Within our framework, the transduction problem is formulated in terms of a non-cooperative multi-player game where any equilibrium of the proposed game corresponds to a consistent labeling of the data. An attractive feature of our formulation is that it is inherently a multi-class approach and imposes no constraint whatsoever on the structure of the pairwise similarity matrix, being able to naturally deal with asymmetric and negative similarities alike. We evaluated our approach on some real-world problems involving symmetric or asymmetric similarities and obtained competitive results against state-of-the-art algorithms.