In this article I address the reception of game-theoretic methods in political science. In particular I challenge the notion that such methods afford a plausible basis for what is commonly called ‘positive political theory’ (PPT). The standard rationale for PPT suggests that the point of formal models is, starting from ‘the’ rationality assumption, to derive predictions that can then be tested empirically. I argue that this standard rationale is hopelessly confused. The confusion stems from the assumption that game-theoretic models are empirically testable in some direct sense. This view is far from unanimously accepted among game theorists outside political science. I argue instead that game-theoretic models are best understood as tools for exploring the operation and limits of one set of basic causal mechanisms. I show how this works in practice and on that basis reassert the value of formal models in political science.