<p>You could represent the game in extensive form like this:</p>

<p><a href="https://i.sstatic.net/wCcn4.png" rel="noreferrer"><img src="https://i.sstatic.net/wCcn4.png" alt="enter image description here"></a></p>

<p>The dashed lines enclose player 2's information set. This encompasses all of player 2's nodes because player 2 observes neither nature's nor player 1's choice. Player 1's information sets are the two singleton nodes because player 1 knows which branch nature has chosen.</p>

CC BY-SA 4.0
2019-06-23T12:34:34.290Z
Thank you! This is exactly what I was looking for. If Player 2 knows which game is played as well I'd circle the first two branches and last to branches, right? If Player 2 doesn't know which game is played, but which action Player 1 took, I'd connect the first and third branch and the second and forth branch, right?
user7802048
CC BY-SA 4.0
2019-06-23T12:35:59.197Z
@user7802048 yes, that's right
Ubiquitous
CC BY-SA 4.0
2019-06-23T12:29:42.783Z
2019-06-23T12:29:42.783Z
Ubiquitous
<p>I'm confronted with the following situation: </p>

<p>First of all nature decides which of two games is played. Then each of two players make a simultaneous move, but only player I knows which game is played. </p>

<p>How can I display this information in extensive form?</p>

<p>The root will be the nature, which decides whether Game I or Game II is played. Now we have two additional layers for each game. Now I would use an information set to display that the moves are taken simultaneously, but how can I display that only player I knows about which game is played?</p>

<game-theory><bayesian-game><extensive-games>
Confusion about multiple information Sets
user7802048
# Confusion about multiple information Sets

(Asked by: username_0 on 2019-06-23)

I'm confronted with the following situation:

First of all nature decides which of two games is played. Then each of two players make a simultaneous move, but only player I knows which game is played.

How can I display this information in extensive form?

The root will be the nature, which decides whether Game I or Game II is played. Now we have two additional layers for each game. Now I would use an information set to display that the moves are taken simultaneously, but how can I display that only player I knows about which game is played?

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

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## 1 answers

### Answer by username_1 on 2019-06-23. Score: 5 | Accepted answer

You could represent the game in extensive form like this:

[![enter image description here](https://i.sstatic.net/wCcn4.png)](https://i.sstatic.net/wCcn4.png)

The dashed lines enclose player 2's information set. This encompasses all of player 2's nodes because player 2 observes neither nature's nor player 1's choice. Player 1's information sets are the two singleton nodes because player 1 knows which branch nature has chosen.

> **Comments:**
> **username_0**: Thank you! This is exactly what I was looking for. If Player 2 knows which game is played as well I'd circle the first two branches and last to branches, right? If Player 2 doesn't know which game is played, but which action Player 1 took, I'd connect the first and third branch and the second and forth branch, right?  
> **username_1**: @user7802048 yes, that's right  

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