 Part of the uncertainty the agents might have about their situation is whether or not all agents are rational. But if it is assumed that all agents are \(\omega\)-Bayesian rational at each \(\omega \in \Omega\), then a description of this fact forms part of the description of each possible \(\omega\) and thus lies in the meet of the agents’ partitions. As noted already, descriptions of the agents’ priors, their partitions and the game also form part of the description of each possible world, so propositions corresponding to these facts also lie in the meet of the agents’ partitions. So another way of stating Aumann’s main result is as follows: Common knowledge of \(\omega\)-Bayesian rationality at each possible world implies that the agents follow an Aumann correlated equilibrium.