Looking again at Figure 1, one can ask what would happen if Bob knew (that is had correct beliefs about) Ann’s strategy choice? Intuitively, it is quite clear that his rational choice is to coordinate with her. If he knows that she plays \(t\), for instance, then playing \(l\) is clearly the only rational choice for him, and similarly, if he knows that she plays \(b\), then \(r\) is the only rational choice. The situation is symmetric for Ann. For instance, if she knows that Bob plays \(l\), then her only rational choice is to choose \(t\). More formally, the only states where Ann is rational and her type knows (i.e., is correct and assigns probability 1 to) Bob’s strategy choice and where Bob is also rational and his type knows Ann’s strategy choices are states where they play either \((t,l)\) or \((b,r)\), the pure-strategy Nash equilibria of the game.