But then, \((O_2)\) is the only strategy that is rational for \(B\) at \(v_2\) in any state \(w\) (this follows since \(u_B(o_2)=2\ge 1=u_B(o_3)\)). This means that if \(w\in \mathsf{Rat}_B\) and \(\Pi_B(w)\subseteq \mathsf{Rat}_A\), then \(\sigma_B(w)(v_2)=O_2\). Finally, if \(A\) knows that \(B\) knows that \(A\) is substantively rational, then