<p>Put player 2's decision nodes after a Left move by player 1 into an information set to concur with the description in bold.
<a href="https://i.sstatic.net/lHpRN.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/lHpRN.jpg" alt="Here..."></a></p>

CC BY-SA 4.0
2020-03-03T10:57:35.183Z
Downvote by me. I percieve these types of answers as giving the man a fish, rather than teaching them to fish (or do game theory).
Giskard
CC BY-SA 4.0
2020-03-03T11:56:39.483Z
@Giskard, well, in some sense I understand the rule here to be: Give them fish, if they have shown at least a minimal amount of fishing effort. Might be a knife-edge case though...
VARulle
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2020-03-03T11:57:42.003Z
Knife-edge? What exactly is the effort made here?
Giskard
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2020-03-03T11:58:57.027Z
Also, ideally you never give the fish, I stick to teaching fishing when possible.
Giskard
CC BY-SA 4.0
2020-03-03T13:51:13.033Z
@Giskard, the effort is in drawing a game tree that is almost correct, accompanied by text without typos and grammatical mistakes. That's considerably more than most of the pls-solve-my-homework questions here have to offer. As for fishing, well, there are different philosophies out there...
VARulle
CC BY-SA 4.0
2020-03-03T15:03:51.847Z
Thanks. In particular, I was confused about the information set crossing over the strategies. So I amended the tree such that I have Left Left side by side.
user508281
CC BY-SA 4.0
2020-03-03T15:05:14.850Z
Also, now technically player 2 plays thrice in the game and would have 8 strategies whereas player 1 plays once and have two strategies (Right or Left). Am I correct?
user508281
CC BY-SA 4.0
2020-03-05T09:07:02.683Z
@user508281, yes, that's correct.
VARulle
CC BY-SA 4.0
2020-03-03T10:27:08.383Z
2020-03-03T10:27:08.383Z
VARulle
<p>Imagine you're Player 2. What different "scenarios" could you find yourself in?</p>

<ul>
<li>If Player 1 chooses Right, then Player 2 could observe if Nature played Up or Down. So you have 2 information sets there.</li>
<li>If Player 1 chooses Left, then Player 2 couldn't differentiate between (Up, Left) and (Down, Left). How many information sets should there be here?</li>
</ul>

<p>So in total, you should have how many information sets? You currently have 4. Which one should you "combine"?</p>

CC BY-SA 4.0
2020-03-03T03:51:59.087Z
2020-03-03T03:51:59.087Z
Art
<p>Question: Represent the extensive form of the game:</p>

<p>Suppose, Nature chooses either Up or Down with probabilities 0.5 and 0.5, respectively. </p>

<p>Then Player 1 chooses either Right or Left and does not observe nature's choice. </p>

<p>Finally, Player 2 chooses either G or H. Unlike Player 1, Player 2 observes the choice of Player 1 prior to making his choice. Player 2 also observes nature's choice if Player 1 has chosen Right <strong>but does not observe nature's choice if Player 1 has chosen Left.</strong> </p>

<p>My take: 
<a href="https://i.sstatic.net/i3sMZ.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/i3sMZ.jpg" alt="enter image description here"></a></p>

<p>Is this correct? I am not really sure about the instructions in bold. </p>

CC BY-SA 4.0
2020-03-02T21:46:54.910Z
You pretty much disregarded the instructions in bold. What exactly is it that you are "not sure about" in that part?
Giskard
CC BY-SA 4.0
2020-03-02T22:31:22.233Z
How to reflect that in the extensive form?
user508281
CC BY-SA 4.0
2020-03-02T22:50:57.433Z
With information sets where needed.
Giskard
CC BY-SA 4.0
2020-03-02T23:03:30.830Z
Can you please be a bit more helpful? That is where I got stuck.
user508281
CC BY-SA 4.0
2020-03-03T02:04:06.847Z
Remember that nodes in the same information set of a player are nodes which the player cannot distinguish. Should there be any such nodes for Player 2 in your example? (i.e. are there any "situations" which Player 2 cannot tell apart?)
pegasus
CC BY-SA 4.0
2020-03-03T03:03:53.923Z
Does it imply that for P2 I need to draw two information sets?
user508281
<game-theory><extensive-games>
Extensive Form Representation
user508281
# Extensive Form Representation

(Asked by: username_0 on 2020-03-02)

Question: Represent the extensive form of the game:

Suppose, Nature chooses either Up or Down with probabilities 0.5 and 0.5, respectively.

Then Player 1 chooses either Right or Left and does not observe nature's choice.

Finally, Player 2 chooses either G or H. Unlike Player 1, Player 2 observes the choice of Player 1 prior to making his choice. Player 2 also observes nature's choice if Player 1 has chosen Right **but does not observe nature's choice if Player 1 has chosen Left.**

My take:
[![enter image description here](https://i.sstatic.net/i3sMZ.jpg)](https://i.sstatic.net/i3sMZ.jpg)

Is this correct? I am not really sure about the instructions in bold.

**Tags:** game-theory, extensive-games

> **Comments:**
> **username_1**: You pretty much disregarded the instructions in bold. What exactly is it that you are "not sure about" in that part?  
> **username_0**: How to reflect that in the extensive form?  
> **username_1**: With information sets where needed.  
> **username_0**: Can you please be a bit more helpful? That is where I got stuck.  
> **username_2**: Remember that nodes in the same information set of a player are nodes which the player cannot distinguish. Should there be any such nodes for Player 2 in your example? (i.e. are there any "situations" which Player 2 cannot tell apart?)  
> **username_0**: Does it imply that for P2 I need to draw two information sets?  

---

## 2 answers

### Answer by username_3 on 2020-03-03. Score: -1 | Accepted answer

Put player 2's decision nodes after a Left move by player 1 into an information set to concur with the description in bold.
[![Here...](https://i.sstatic.net/lHpRN.jpg)](https://i.sstatic.net/lHpRN.jpg)

> **Comments:**
> **username_1**: Downvote by me. I percieve these types of answers as giving the man a fish, rather than teaching them to fish (or do game theory).  
> **username_3**: @username_1, well, in some sense I understand the rule here to be: Give them fish, if they have shown at least a minimal amount of fishing effort. Might be a knife-edge case though...  
> **username_1**: Knife-edge? What exactly is the effort made here?  
> **username_1**: Also, ideally you never give the fish, I stick to teaching fishing when possible.  
> **username_3**: @username_1, the effort is in drawing a game tree that is almost correct, accompanied by text without typos and grammatical mistakes. That's considerably more than most of the pls-solve-my-homework questions here have to offer. As for fishing, well, there are different philosophies out there...  
> **username_0**: Thanks. In particular, I was confused about the information set crossing over the strategies. So I amended the tree such that I have Left Left side by side.  
> **username_0**: Also, now technically player 2 plays thrice in the game and would have 8 strategies whereas player 1 plays once and have two strategies (Right or Left). Am I correct?  
> **username_3**: @username_0, yes, that's correct.  

---

### Answer by username_4 on 2020-03-03. Score: 1

Imagine you're Player 2. What different "scenarios" could you find yourself in?

* If Player 1 chooses Right, then Player 2 could observe if Nature played Up or Down. So you have 2 information sets there.
* If Player 1 chooses Left, then Player 2 couldn't differentiate between (Up, Left) and (Down, Left). How many information sets should there be here?

So in total, you should have how many information sets? You currently have 4. Which one should you "combine"?


---

