 This statement is the negation, for each player, of her current action being strongly dominated. Naturally, this property can be expressed formally with suitable epistemic action modalities. Yet, even as it stands, it is clear that Weak Rationality can be announced to prune away strategy profiles, and that in a iterated manner. The strategic game will change every time weak rationality is announced, initiating a stepwise process that resembles the earlier iterative announcements of rationality for Backward Induction. As observed there, limits of public announcements are always reached eventually, as models can only get smaller. For announcing Weak Rationality, these limits match the outcome of \(SD^\infty\) precisely (van Benthem 2007).