Consider the following extensive-form game:
In one alternative, Player 2 chooses G and E and Player 1 chooses D. However, Player 2 can increase her gain by making a credible threat and switch from G to H, prompting Player 1 to play C.
Are credible threats accounted for in the SPNE / backward induction framework? Would (D, {E, G}) be considered a subgame perfect equilibrium? How many subgame perfect equilibria are there in this game?
In fact, a major point of subgame perfect equilibrium is to decide which threats are credible and which aren't. You may a threat, but when it comes time to play that strategy, it is not in your interest, so you don't do it, and the threat is not credible, assuming @Mark Saving there is not a commitment technology. The game above is actually not a great game to look at SPNE, because player 2 is always indifferent between either action. (D,(E,G))is subgame perfect, because when 2 gets to play, E or G is (weakly) the best action.