<p><a href="https://i.sstatic.net/d4aPC.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/d4aPC.png" alt="enter image description here"></a></p>

<p>First picture: we always do the roll back scenario, (B,M,F) so Francisco start and 2 > 0 in the last node so therefore he will be in.</p>

<p>And if Franscisco is in, McDonalds at the last node, have to choose to fight or coop, and since 4 > 2, they will coop. </p>

<p>And at McDonalds first node, he will coop since fight will have a payoff of 0. </p>

<p>And first node, Bobs burger, he choose in because if he is out he will get 0. </p>

<p>Is this correct?</p>

<p>And when it comes to this: </p>

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

<p>We look at player 3's payoff, shown with the highlighted lines.</p>

<p>And then player 2, will choose F since it is his best payoff at that node</p>

<p>And then we look at player 2 again at the second node, he will choose  D since it is his best payoff, </p>

<p>And then last, at the first node, player 1, he will choose  A since it is his best payoff?</p>

<p>And therefore the correct answer is (A). </p>

<p>Is it right? </p>

CC BY-SA 4.0
2020-03-12T06:44:12.617Z
In the second game, why would P2 choose F? P2 gets 1 if he chooses F, but what if he chooses E?
Herr K.
CC BY-SA 4.0
2020-03-12T08:33:45.297Z
@HerrK. I think that he should play F because if he chooses E, he will get pay off of 2 or 0.. And if he goes F he would get a pay off of 1 or 5?
soet irl
CC BY-SA 4.0
2020-03-12T10:54:13.727Z
@soetirl: You highlighted the choice of X by P3, meaning that if P3 gets to choose, he will choose X. Now if P2 chooses E, what will happen next?
VARulle
CC BY-SA 4.0
2020-03-12T11:18:52.273Z
@VARulle If P2 chooses E he will get a pay off of 2. But If he P2 choose D he will get a payoff of 3? 3 > 2 :(
soet irl
CC BY-SA 4.0
2020-03-12T11:26:00.803Z
@soetirl: Yes, but I'm talking about P2's second decision node here. If he chooses E, he gets 2. If he instead chooses F, what does he get? So which of the two possible choices at his second node is better, E or F?
VARulle
CC BY-SA 4.0
2020-03-12T12:24:09.230Z
He, P2, gets 1 if he chooses F. And 2 if he choose E. So he should probably go E. And then he, P2 , at P2's choises between  C or D. He should go D?
soet irl
CC BY-SA 4.0
2020-03-12T12:35:01.507Z
@VARulle He, P2, gets 1 if he chooses F. And 2 if he choose E. So he should probably go E. And then he, P2 , at P2's choises between C or D. He should go D?
soet irl
CC BY-SA 4.0
2020-03-12T12:49:05.410Z
@soetirl: Right. And that's why your argument *"And then player 2, will choose F since it is his best payoff at that node"* should be corrected and why E should be highlighted instead of F. (At his first node, P2 should choose D, that's correct.)
VARulle
CC BY-SA 4.0
2020-03-12T14:22:12.207Z
@VARulle so the SPNE in this game is therefore (4,3,1) ::...... P1 plays A, P2 plays D, P3 plays X. So the correct answer here is (A) ?
soet irl
CC BY-SA 4.0
2020-03-12T15:18:55.303Z
@soetirl: (4,3,1) is the SPNE outcome. The sequence A, D is the SPNE path. The SPNE itself is what is described in solution (A) and could be written as (A,DE,X).
VARulle
CC BY-SA 4.0
2020-03-13T10:35:20.803Z
@VARulle Okej, but then when it comes the McDonalds tree (first image)  we start with McDonalds, (P3), he will choose to coop in the last node, because 4 > 2. 

And then we have Fransicso (P2) he will choose out, since 7 > 2.

And then we have McDonalds again, he will choose - what? Fight or coop, since he will get payoff of 0 in either nodes of the nodes there?
soet irl
CC BY-SA 4.0
2020-03-13T11:58:47.467Z
@soetirl: There is no 7 in Francisco's payoffs...
VARulle
CC BY-SA 4.0
2020-03-13T13:07:41.217Z
@VARulle ahh it says (B,M,F).. So. We start with McDonald’s at the last node right? He get to choose between fight or coop, and he chooses to coop since 4>2.

Then we look at Franscico, at his node he get to choose between out or in. And He chooses in since he get a pay off of 0 if he’s out. 

Then we look at McDonald’s again, and there them have to decide to fight or coop. And they choose coop since otherwise they get a payoff of 0. 

And last one, Bobs burger, he choose in, otherwise he get a pay off of 0.
soet irl
CC BY-SA 4.0
2020-03-13T13:12:59.240Z
So therefore the correct answer is (2,4,2) right?
soet irl
CC BY-SA 4.0
2020-03-13T15:07:53.670Z
@soetirl: No, the answer is the highlighted one, (C), or the profile (IN, COCO, IN).
VARulle
<game-theory>
SPNE with 3 players in a three
soet irl
# SPNE with 3 players in a three

(Asked by: username_0 on 2020-03-11)

[![enter image description here](https://i.sstatic.net/d4aPC.png)](https://i.sstatic.net/d4aPC.png)

First picture: we always do the roll back scenario, (B,M,F) so Francisco start and 2 > 0 in the last node so therefore he will be in.

And if Franscisco is in, McDonalds at the last node, have to choose to fight or coop, and since 4 > 2, they will coop.

And at McDonalds first node, he will coop since fight will have a payoff of 0.

And first node, Bobs burger, he choose in because if he is out he will get 0.

Is this correct?

And when it comes to this:

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

We look at player 3's payoff, shown with the highlighted lines.

And then player 2, will choose F since it is his best payoff at that node

And then we look at player 2 again at the second node, he will choose D since it is his best payoff,

And then last, at the first node, player 1, he will choose A since it is his best payoff?

And therefore the correct answer is (A).

Is it right?

**Tags:** game-theory
> **Comments:**
> **username_1**: In the second game, why would P2 choose F? P2 gets 1 if he chooses F, but what if he chooses E?  
> **username_0**: @HerrK. I think that he should play F because if he chooses E, he will get pay off of 2 or 0.. And if he goes F he would get a pay off of 1 or 5?  
> **username_2**: @soetirl: You highlighted the choice of X by P3, meaning that if P3 gets to choose, he will choose X. Now if P2 chooses E, what will happen next?  
> **username_0**: @VARulle If P2 chooses E he will get a pay off of 2. But If he P2 choose D he will get a payoff of 3? 3 > 2 :(  
> **username_2**: @soetirl: Yes, but I'm talking about P2's second decision node here. If he chooses E, he gets 2. If he instead chooses F, what does he get? So which of the two possible choices at his second node is better, E or F?  
> **username_0**: He, P2, gets 1 if he chooses F. And 2 if he choose E. So he should probably go E. And then he, P2 , at P2's choises between  C or D. He should go D?  
> **username_0**: @VARulle He, P2, gets 1 if he chooses F. And 2 if he choose E. So he should probably go E. And then he, P2 , at P2's choises between C or D. He should go D?  
> **username_2**: @soetirl: Right. And that's why your argument *"And then player 2, will choose F since it is his best payoff at that node"* should be corrected and why E should be highlighted instead of F. (At his first node, P2 should choose D, that's correct.)  
> **username_0**: @VARulle so the SPNE in this game is therefore (4,3,1) ::...... P1 plays A, P2 plays D, P3 plays X. So the correct answer here is (A) ?  
> **username_2**: @soetirl: (4,3,1) is the SPNE outcome. The sequence A, D is the SPNE path. The SPNE itself is what is described in solution (A) and could be written as (A,DE,X).  
> **username_0**: @VARulle Okej, but then when it comes the McDonalds tree (first image)  we start with McDonalds, (P3), he will choose to coop in the last node, because 4 > 2.   And then we have Fransicso (P2) he will choose out, since 7 > 2.  And then we have McDonalds again, he will choose - what? Fight or coop, since he will get payoff of 0 in either nodes of the nodes there?  
> **username_2**: @soetirl: There is no 7 in Francisco's payoffs...  
> **username_0**: @VARulle ahh it says (B,M,F).. So. We start with McDonald’s at the last node right? He get to choose between fight or coop, and he chooses to coop since 4>2.  Then we look at Franscico, at his node he get to choose between out or in. And He chooses in since he get a pay off of 0 if he’s out.   Then we look at McDonald’s again, and there them have to decide to fight or coop. And they choose coop since otherwise they get a payoff of 0.   And last one, Bobs burger, he choose in, otherwise he get a pay off of 0.  
> **username_0**: So therefore the correct answer is (2,4,2) right?  
> **username_2**: @soetirl: No, the answer is the highlighted one, (C), or the profile (IN, COCO, IN).  

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## 0 answers

