<p>Does a mechanical set of rules or algorithm exist for doing forward induction on a game tree, or is it an &quot;every problem is too unique and requires its own reasoning&quot; 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 &quot;Game Theory 101 The Complete Textbook&quot; by William Spaniel...</p>
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<p>As I try to solve this problem, as soon as I get to, &quot;Player 1's payoff of <span class="math-container">$1$</span> for defenestration still beats both <span class="math-container">$0$</span> and <span class="math-container">$-2$</span>,&quot; I delete Player 1 swerving from the overall game tree, yielding...</p>
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<p>...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.</p>
<p>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.</p>

CC BY-SA 4.0
2022-11-23T08:47:29.960Z
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.
VARulle
CC BY-SA 4.0
2022-11-23T08:52:40.470Z
There is no unique commonly accepted definition of forward induction.
Michael Greinecker
CC BY-SA 4.0
2022-11-23T10:18:21.323Z
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?
Oliver Queen
CC BY-SA 4.0
2022-11-25T08:59:48.847Z
@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.
VARulle
CC BY-SA 4.0
2022-11-25T18:07:11.383Z
@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.
user10478
CC BY-SA 4.0
2022-11-26T09:27:38.027Z
You're right, it shouldn't matter as a method for solving the game, at least in this simple case (where it is uncontroversial what "forward induction" entails). In this respect it's true that your method is just a shortcut to the elaborate explanation in the book.
VARulle
CC BY-SA 4.0
2022-11-26T11:13:11.880Z
@VARulle Here it is something about forward utility criteria
http://www.statslab.cam.ac.uk/~mike/papers/forward-utilities.pdf
Oliver Queen
CC BY-SA 4.0
2022-11-26T13:04:07.460Z
@OliverQueen, the term "forward utility criteria" doesn't appear in this paper either. But yes, it's about "forward utility", a term from mathematical finance which has nothing to do with forward induction.
VARulle
<game-theory><algorithms><methodology><textbooks><solution-concept>
Forward Induction Procedure
user10478
# Forward Induction Procedure

(Asked by: username_0 on 2022-11-23)

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...

[![enter image description here](https://i.sstatic.net/LZbxk.jpg)](https://i.sstatic.net/LZbxk.jpg)
[![enter image description here](https://i.sstatic.net/AhGys.jpg)](https://i.sstatic.net/AhGys.jpg)

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...

[![enter image description here](https://i.sstatic.net/dSc14.png)](https://i.sstatic.net/dSc14.png)

...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.

**Tags:** game-theory, algorithms, methodology, textbooks, solution-concept

> **Comments:**
> **username_1**: 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.  
> **username_2**: There is no unique commonly accepted definition of forward induction.  
> **username_3**: 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?  
> **username_1**: @username_3, 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.  
> **username_0**: @username_1 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.  
> **username_1**: You're right, it shouldn't matter as a method for solving the game, at least in this simple case (where it is uncontroversial what "forward induction" entails). In this respect it's true that your method is just a shortcut to the elaborate explanation in the book.  
> **username_3**: @username_1 Here it is something about forward utility criteria http://www.statslab.cam.ac.uk/~mike/papers/forward-utilities.pdf  
> **username_1**: @username_3, the term "forward utility criteria" doesn't appear in this paper either. But yes, it's about "forward utility", a term from mathematical finance which has nothing to do with forward induction.  

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## 0 answers

