The extent of this conflict is nicely illustrated in Samuelson (1992). In particular, Samuelson (1992) shows that there is no epistemic-probability  model[14]  of the above game with a state satisfying common knowledge of rationality (where “rationality” means that players do not choose weakly dominated strategies). Prima facie, this is puzzling: What about the epistemic-probability model consisting of a single state \(w\) assigned the profile \((u, l)\)? Isn’t this a model of the above game where there is a state satisfying common knowledge that the players do not choose weakly dominated strategies? The problem is that the players do not have “cautious” beliefs in this model (in particular, Bob’s beliefs are not cautious in the sense described below). Recall that having a cautious belief means that a player cannot know which options her opponent(s) will  pick[15]  from a set of choice-worthy options (in the above game, if Ann knows that Bob is choosing \(l\), then both \(u\) and \(d\) are “choice-worthy”, so Bob cannot know that Ann is choosing \(u\)). This suggests an additional requirement on a game model: Let \(\M=\epprobmodel\) be an epistemic-probability model. For each action \(a\in \cup_{i\in\Agt} S_i\), let \({[\![{a}]\!]}=\{w \mid (\sigma(w))_i=a\}\).