This article presents a new approach to understanding strategic decision making inspired by the mathematics of quantum theory. Empirical support for this new approach is based on five different puzzling findings from past work on the prisoner dilemma game including the disjunction effect, the interference of predictions on actions in simultaneous and sequential games, question order effect, and the effects of cheap promises. Eight different quantum models are described, which purport to account for these puzzling findings. The competing models are systematically compared with respect to their capability of accounting for the five empirical findings.