<p>Step 1.</p>

<p>Determine strategies.</p>

<p>Step 2. </p>

<p>Calculate payoffs for strategy profiles.</p>

<p>Step 3.</p>

<p>Write normal form.</p>

CC BY-SA 4.0
2019-11-27T22:16:39.253Z
Would it be the same as if the information set was not there? (I mean "as if the two nodes in the information set are in separate information set").
Aqqqq
CC BY-SA 4.0
2019-11-27T22:17:14.987Z
No. If you do not understand what strategies are, please consult your textbook.
Giskard
CC BY-SA 4.0
2019-11-27T22:21:09.090Z
I only know that their strategies are respectively: Player 1: Up, Uq, Dp, Dq; Player 2: TL, TR, BL, BR. Can you tell me my mistake?
Aqqqq
CC BY-SA 4.0
2019-11-27T22:23:37.063Z
Yes: your mistake is that these are not the strategies with imperfect information. Please consult your textbook.
Giskard
CC BY-SA 4.0
2019-11-27T22:32:36.927Z
Does it mean that I need to make assumption about belief before deriving the appropriate strategy?
Aqqqq
CC BY-SA 4.0
2019-11-27T22:34:06.160Z
Which textbook told you that? Please name your source (title and page number).
Giskard
CC BY-SA 4.0
2019-11-27T22:08:13.697Z
2019-11-27T22:08:13.697Z
Giskard
<p>The dimension of the normal form game derived from an extensive form is given by the number of pure strategies each player has. </p>

<p>Generally speaking, the number of pure strategies a player has in an extensive form game equals the product of the number of actions at each information set where she moves. Suppose a player moves at <span class="math-container">$N$</span> information sets on a game tree, and at each information set <span class="math-container">$n$</span> there are <span class="math-container">$m_n$</span> actions, then she has <span class="math-container">$m_1\times m_2\times\cdots\times m_N$</span> number of pure strategies.</p>

<p>In your example, <span class="math-container">$N=2$</span>, <span class="math-container">$m_1=m_2=2$</span> for player 1; and <span class="math-container">$N=1$</span>, <span class="math-container">$m_1=2$</span> for player 2. So the normal form game corresponding to your game tree should be a <span class="math-container">$4\times2$</span> matrix.</p>

<p><a href="http://www.sfu.ca/~shihenl/302/Strategies%20Memo.pdf" rel="nofollow noreferrer">This note</a> describes a step-by-step procedure that's relatively easy to follow. </p>

CC BY-SA 4.0
2019-11-28T18:08:47.623Z
The note lists the same steps that I do...
Giskard
CC BY-SA 4.0
2019-11-28T19:16:01.543Z
@Giskard: Yes, but with a little bit more detail `:)`
Herr K.
CC BY-SA 4.0
2019-11-28T17:02:51.753Z
2019-11-28T17:02:51.753Z
Herr K.
<p>How can we write down a normal form for this following game with information set?</p>

<p>(The picture is modified from a picture from Wikipedia.)
<a href="https://i.sstatic.net/Owy7F.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Owy7F.jpg" alt="enter image description here"></a></p>

CC BY-SA 4.0
2019-11-28T03:31:41.533Z
A player cannot have different actions at different nodes of an information set. In particular, Player 2 cannot have {T,B} at the top node of his information set and {L,R} at the bottom node.
Herr K.
CC BY-SA 4.0
2019-11-28T11:12:18.603Z
Thank you for the information. Would the current game work?
Aqqqq
CC BY-SA 4.0
2019-11-28T11:16:57.690Z
@HerrK. So the strategies to be included in the normal form is: Player 1: Up, Uq, Dp, Dq; 
Player 2: T, B?
Aqqqq
<game-theory>
How to write down a normal form of the game with information set?
Aqqqq
# How to write down a normal form of the game with information set?

(Asked by: username_0 on 2019-11-27)

How can we write down a normal form for this following game with information set?

(The picture is modified from a picture from Wikipedia.)
[![enter image description here](https://i.sstatic.net/Owy7F.jpg)](https://i.sstatic.net/Owy7F.jpg)

**Tags:** game-theory

> **Comments:**
> **username_1**: A player cannot have different actions at different nodes of an information set. In particular, Player 2 cannot have {T,B} at the top node of his information set and {L,R} at the bottom node.  
> **username_0**: Thank you for the information. Would the current game work?  
> **username_0**: @HerrK. So the strategies to be included in the normal form is: Player 1: Up, Uq, Dp, Dq;  Player 2: T, B?  

---

## 2 answers

### Answer by username_1 on 2019-11-28. Score: 2 | Accepted answer

The dimension of the normal form game derived from an extensive form is given by the number of pure strategies each player has.

Generally speaking, the number of pure strategies a player has in an extensive form game equals the product of the number of actions at each information set where she moves. Suppose a player moves at $N$ information sets on a game tree, and at each information set $n$ there are $m\_n$ actions, then she has $m\_1\times m\_2\times\cdots\times m\_N$ number of pure strategies.

In your example, $N=2$, $m\_1=m\_2=2$ for player 1; and $N=1$, $m\_1=2$ for player 2. So the normal form game corresponding to your game tree should be a $4\times2$ matrix.

[This note](http://www.sfu.ca/~shihenl/302/Strategies%20Memo.pdf) describes a step-by-step procedure that's relatively easy to follow.

> **Comments:**
> **username_2**: The note lists the same steps that I do...  
> **username_1**: @username_2: Yes, but with a little bit more detail `:)`  

---

### Answer by username_2 on 2019-11-27. Score: 1

Step 1.

Determine strategies.

Step 2.

Calculate payoffs for strategy profiles.

Step 3.

Write normal form.

> **Comments:**
> **username_0**: Would it be the same as if the information set was not there? (I mean "as if the two nodes in the information set are in separate information set").  
> **username_2**: No. If you do not understand what strategies are, please consult your textbook.  
> **username_0**: I only know that their strategies are respectively: Player 1: Up, Uq, Dp, Dq; Player 2: TL, TR, BL, BR. Can you tell me my mistake?  
> **username_2**: Yes: your mistake is that these are not the strategies with imperfect information. Please consult your textbook.  
> **username_0**: Does it mean that I need to make assumption about belief before deriving the appropriate strategy?  
> **username_2**: Which textbook told you that? Please name your source (title and page number).  

---

