I have read a book saying that "... backward induction cannot be applied to games of imperfect or incomplete information because this entails cutting through non-singleton information sets."
However, in another textbook, it says that backward induction can be applied to games of imperfect information, and we can derive the equilibrium by starting at a historical point and show the subgame perfect equilibrium in that subgame is a equilibrium in the Nash equilibrium.
I wonder what are the contexts to use backward induction in a game with imperfect information but complete information?