Notice that since \(\Pi_B(w')=\{\{w'\}\}\subseteq U\) we have \(w'\in K_B(U)\). That is, Bob knows that Ann chooses \(u\) at state \(w'\). Finally, a simple calculation shows that \(w_1\in -K_A(-K_B(U))\), as desired. Of course, we can question the other substantive assumptions built-in to this model (e.g., at \(w_1\), Bob knows that Ann does not know he will choose \(L\)) and continue modifying the model. This raises a number of interesting conceptual and technical issues which we discuss in Section 7.