Consider the state \((d,r,a_3,b_3)\). Both \(a_3\) and \(b_3\) correctly believe (i.e., assign probability 1 to) that the outcome is \((d,r)\) (we have \(\lambda_A(a_3)(r)=\lambda_B(b_3)(d)=1\)). This fact is not common knowledge: \(a_3\) assigns a 0.5 probability to Bob being of type \(b_2\), and type \(b_2\) assigns a 0.5 probability to Ann playing \(l\). Thus, Ann does not know that Bob knows that she is playing \(r\) (here, “knowledge” is identified with “probability 1” as it is in Aumann &amp; Brandenburger 1995). Furthermore, while it is true that both Ann and Bob are rational, it is not common knowledge that they are rational. Indeed, the type \(a_3\) assigns a 0.5 probability to Bob being of type \(b_2\) and choosing \(r\); however, this is irrational since \(b_2\) believes that both of Ann’s options are equally probable.