# Forward Induction Procedure

Does a mechanical set of rules or algorithm exist for doing forward induction on a game tree, or is it an "every problem is too unique and requires its own reasoning" type of situation? I have seen a few examples of forward induction explained, but with pretty basic game trees, and I fear I may be using inapplicable logic yet still reaching the correct strategy vector. Here's an example from the book "Game Theory 101 The Complete Textbook" by William Spaniel...

As I try to solve this problem, as soon as I get to, "Player 1's payoff of $$1$$ for defenestration still beats both $$0$$ and $$-2$$," I delete Player 1 swerving from the overall game tree, yielding...

...which is trivial to solve using backward induction. However, the book's explanation reconsiders that Player 1 might swerve in the final paragraph and corresponding game tree, only using the irrationality of Player 1 swerving in the step immediately following the observation.

It's possible that my issue is more so with dashed lines in game trees than the actual forward induction. I know they represent simultaneous elements of sequential games, but I'm not sure if any operations for simplifying game trees become invalid in the presence of simultaneity.

• The book seems to have an awkward way of presenting "partial game trees" to support its arguments. However, your "simplified" game tree is one of perfect information, i.e. player 2 observes player 1's decision of C. But this is not what happens. Rather, player 2 only infers (by forward induction) player 1's decision of C from him not having chosen D. Commented Nov 23, 2022 at 8:47
• There is no unique commonly accepted definition of forward induction. Commented Nov 23, 2022 at 8:52
• Is forward induction related to the forward utility criteria as well? And why should we consider it instead of backward induction? What are the pros? Commented Nov 23, 2022 at 10:18
• @OliverQueen, I'd answer your first question with NO, just because I have never heard of "forward utility criteria". Your other questions should be posted as genuine question, this comment section is not the right place for them. Commented Nov 25, 2022 at 8:59
• @VARulle With respect to your first comment, does the distinction actually matter in terms of solving more complicated games? In simple backward induction, for example, we remove branches at the end of the game that will not be chosen in light of their payoffs, as though earlier players actually observed the choice made. Of course, if the rationality assumptions behind any solution concept fail then all bets are off. Commented Nov 25, 2022 at 18:07