If Ann is assigned the type \(t_2^A\), then Ann believes that Bob believes that Ann believes that Bob will choose \(l\). Note that type \(t_2^A\) “believes” that Bob will choose \(l\) and furthermore \(t_2^A\) believes that Bob is of type \(t^B_2\) who in turn believes that Ann is of type \(t^A_2\).