This result establishes sufficient conditions for ISDS. It has also a converse direction: given any strategy profile that survives iterated elimination of strictly dominated strategies, there is a model in which this profile is played where all players are rational and this is common knowledge. In other words, one can always view or interpret the choice of a strategy profile that would survive the iterative elimination procedure as one that results from common knowledge of rationality. Of course, this form of the converse is not particularly interesting as we can always define a type space where all the players assign probability 1 to the given strategy profile (and everyone playing their requisite strategy). Much more interesting is the question whether the entire set of strategy profiles that survive iteratively removal of strictly dominated strategies is consistent with rationality and common belief in rationality. This is covered by the following theorem of Brandenburger &amp; Dekel (1987) (cf. also Tan &amp; Werlang 1988):