It is not hard to find a game and an informational context where there is at least one player without a unique “rational choice”. How should a rational player incorporate the information that more than one action is classified as “choice-worthy” or “rationally permissible” (according to some choice rule) for her opponent(s)? In such a situation, it is natural to require that the player does not rule out the possibility that her opponent will pick a “choice-worthy” option. More generally, the players should be “cautious” about which of their opponents’ options they rule out.