We can define the event that player \(i\) is substantively rational is the standard way: \(\mathsf{Rat}_i=\{w \mid \mbox{player } i\) is substantively rational at state \(w\}\); and so, the event that all players are substantively rational is \(\mathsf{Rat}=\bigcap_{i\in N} \mathsf{Rat}_i\).