<p>P2 knows where they are, but if P3 plays afterward, they don't.</p>
<p>To see if a subgame starts at a node, check whether any of the weakly later nodes are connected by an information set with a node that does not come weakly later.</p>

CC BY-SA 4.0
2024-05-07T21:14:57.097Z
2024-05-07T21:14:57.097Z
Michael Greinecker
<p>Consider the following extensive form game:</p>
<p><a href="https://i.sstatic.net/fTgYYK6t.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fTgYYK6t.png" alt="enter image description here" /></a></p>
<p>How many subgames are there in this game?</p>
<p>Suggested Solution: There are two subgames. One after P1 plays R and P2 plays r, and then
the whole game.</p>
<p>My question: is there a way to judge whether it is a subgame? I find this answer could be helpful: <a href="https://math.stackexchange.com/questions/657539/how-to-recognize-a-proper-sub-game">https://math.stackexchange.com/questions/657539/how-to-recognize-a-proper-sub-game</a></p>
<p>But why the game here starts at <span class="math-container">$P_2$</span> is not a subgame? <span class="math-container">$P_2$</span> obviously knows where he is.</p>

<game-theory>
How many subgames are there in this game?
PiVoyager
# How many subgames are there in this game?

(Asked by: username_0 on 2024-05-07)

Consider the following extensive form game:

[![enter image description here](https://i.sstatic.net/fTgYYK6t.png)](https://i.sstatic.net/fTgYYK6t.png)

How many subgames are there in this game?

Suggested Solution: There are two subgames. One after P1 plays R and P2 plays r, and then
the whole game.

My question: is there a way to judge whether it is a subgame? I find this answer could be helpful: <https://math.stackexchange.com/questions/657539/how-to-recognize-a-proper-sub-game>

But why the game here starts at $P\_2$ is not a subgame? $P\_2$ obviously knows where he is.

**Tags:** game-theory


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## 1 answers

### Answer by username_1 on 2024-05-07. Score: 1

P2 knows where they are, but if P3 plays afterward, they don't.

To see if a subgame starts at a node, check whether any of the weakly later nodes are connected by an information set with a node that does not come weakly later.


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