Advancing our understanding of human behavior hinges on the ability of theories to unveil the mechanisms underlying such behaviors. Measuring the ability of theories and models to predict unobserved behaviors provides a principled method to evaluate their merit and, thus, to help establish which mechanisms are most plausible. Here, we propose models and develop rigorous inference approaches to predict strategic decisions in dyadic social dilemmas. In particular, we use bipartite stochastic block models that incorporate information about the dilemmas faced by individuals. We show, combining these models with empirical data on strategic decisions in dyadic social dilemmas, that individual strategic decisions are to a large extent predictable, despite not being "rational." The analysis of these models also allows us to conclude that: (i) individuals do not perceive games according their game-theoretical structure; (ii) individuals make decisions using combinations of multiple simple strategies, which our approach reveals naturally.