Assuming that the players’ beliefs are “cautious” is naturally related to weak dominance (recall the characterization of weak dominance, Section 3.2 in which a strategy is weakly dominated iff it does not maximize expected utility with respect to any full support probability measure). A key issue in epistemic game theory is the epistemic analysis of iterated removal of weakly dominated strategies. Many authors have pointed out puzzles surrounding such an analysis (Asheim &amp; Dufwenberg 2003; Brandenburger, Friedenberg &amp; Keisler 2008; Cubitt &amp; Sugden 1994; Samuelson 1992). For example, Samuelson (1992) showed (among other things) that the analogue of Theorem 4.1 is not true for iterated removal of weakly dominated strategies. The main problem is illustrated by the following game: