 Unlike the case of M-implicatures, many Quantity implicatures hinge on the fact that alternative expressions differ with respect to logical strength: the inference from ‘three’ to the pragmatically strengthed ‘exactly three’-reading, that we sketched in Section 1.1, draws on the fact that the alternative expression ‘four’ is semantically stronger, i.e., ‘four’ semantically entails ‘three’, but not the other way around, under the assumed ‘at least’-semantics. In order to bring considerations of semantic strength to bear on game-theoretic pragmatics, we must assign conventional meaning some role in either the game model or the solution concept. In the following, we look at two similar, but distinct possibilities of treating semantic meaning in approaches that spell out pragmatic reasoning as chains of (higher-order) reasoning about interlocutors’ rationality.