There are many different partitions for Ann and Bob that we can use to complete the description of this simple epistemic model. Not all of the partitions are appropriate for analyzing the ex interim stage of the decision-making process, though. For example, suppose \(\Pi_{A}=\Pi_{B}=\{W\}\) and consider the event \(U=\{(u,l),(u,r)\}\) representing the situation where Ann chooses \(u\). Notice that \(K_A(U)=\emptyset\) since for all \(w\in W\), \(\Pi_A(w)\not\subseteq U\), so there is no state where Ann knows that she chooses \(u\). This means that this model is appropriate for reasoning about the ex ante stage rather than the ex interim stage. This is easily fixed with an additional technical assumption: Suppose \(S\) is a set of strategy profiles for some (strategic or extensive) game with players \(\A=\{1,\ldots,n\}\).