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 [imath]1[/imath] for defenestration still beats both [imath]0[/imath] and [imath]-2[/imath]," 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.
As I try to solve this problem, as soon as I get to, "Player 1's payoff of [imath]1[/imath] for defenestration still beats both [imath]0[/imath] and [imath]-2[/imath]," 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.
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