 A straightforward and efficient way of bringing semantic meaning into game-theoretic pragmatics is to simply restrict the set of viable strategies of sender and receiver in a signaling game to those strategies that conform to conventional meaning: a sender can only select forms that are true of the actual state, and the receiver can only select interpretations which are in the denotation of an observed message. This may seem crude and excludes cases of non-literal language use, lying, cheating and error from the start, but it may serve to rationalize common patterns of pragmatic reasoning among cooperative, information-seeking interlocutors. Based on such a restriction to truth-obedient strategies, it has been shown independently by Pavan (2013) and Rothschild (2013) that there is an established non-equilibrium solution concept that nicely rationalizes Quantity implicatures, namely iterated admissibility, also known as iterated elimination of weakly dominated strategies. Without going into detail, the general idea of this solution concept is to start with the whole set of viable strategies (all conforming to semantic meaning) and then to iteratively eliminate all strategies \(X\) for which there is no cautious belief about which of the opponent’s remaining strategies the opponent will likely play that would make \(X\) a rational thing to do. (A cautious belief is one that does not exclude any opponent strategy that has not been eliminated so far.) The set of strategies that survive repeated iterations of elimination are then compatible with (a particular kind of) common belief in rationality. In sum, iterated admissibility is an eliminative approach: starting from the set of all (truth-abiding) strategies, some strategies are weeded out at every step until we remain with a stable set of strategies from which nothing can be eliminated anymore.