Information about the rationality of players at pre-terminal nodes is very important for players choosing earlier in the game. Returning to the game in Figure 17, if \(B\) knows that \(A\) is substantively rational at a state \(w\) in an epistemic model of the game, then \(\Pi_B(w)\subseteq \mathsf{Rat}_A\). Given the above argument, this means that if \(w'\in \Pi_B(w)\), then \(\sigma_A(w')(v_3)=O_3\). Thus, we have for any state \(w\) in an epistemic model of the game,