 A crucial difference between iterated best response approaches and the previously mentioned approach based on iterated admissibility is that the former does not shrink a set of strategies but allows for a different set of best responses at each step. This also makes it so that (some) iterated best response approaches can deal with pragmatic reasoning in cases where interlocutors’ preferences are not aligned, i.e., where the Gricean assumption of cooperativity does not hold, or where there are additional incentives to deviate from semantic meaning (for more about game models for reasoning in non-cooperative contexts, see, e.g., Franke, de Jager &amp; van Rooij 2012, de Jaegher &amp; van Rooij 2014, Franke &amp; van Rooij 2015). Another difference between iterated best response models and iterated admissibility is that the latter do not by itself account for Horn’s division of pragmatic labor (see Franke 2014b and Pavan 2014 for discussion).