There are two main ingredients to the epistemic characterization of iterated weak dominance. The first is to represent the players’ beliefs as lexicographic probability systems. The second is to use a stronger notion of belief: A player assumes an event \(E\) provided \(E\) is infinitely more likely than \(\overline{E}\) (on finite spaces, this means each state in \(E\) is infinitely more likely than states not in \(E\)). The key question is: What is the precise relationship between the event “rationality and common assumption of rationality” and the strategies that survive iterated removal of weakly dominated strategies? The precise answer turns out to be surprisingly subtle—the details are beyond the scope of this article (see Brandenburger et al. 2008).