If a strategy is strictly dominated, it remains so if the player gets more information about what her opponents (might) do. Thus, if a strategy \(s_i\) is strictly dominated in a game \(G\) with respect to the entire set of her opponents’ strategies \(S_{-i}\), then it will never be rational (according to the above definitions) in any epistemic (-plausibility) model for \(G\). I.e., there are no beliefs player \(i\) can have that makes \(s_i\) rational. The same observation does not hold for weak dominance. The existential part of the definition of weak dominance means that the analogue of Observation 3.3 does not hold for weak dominance: if \(s_i\) is weakly dominated with respect to \(X\) then it need not be the case that \(s_i\) is weakly dominated with respect to some \(X'\subseteq X\).