<blockquote>
<p>Every Nash equilibrium is Subgame perfect Nash equilibrium.</p>
</blockquote>
<p>This statement is wrong. I show this by an counter example.</p>
<p><a href="https://i.sstatic.net/tevQn.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/tevQn.jpg" alt="enter image description here" /></a></p>
<p>Is this example enough and good to disprove this statements?</p>
<p>Please share your ideas with me.</p>
<p>Thank you</p>
<p>Note: in the paper, there is typo.</p>
<p>(Out, price war) is not SPNE, but NE. (In, accomodate) is NE and SPNE. So, NE set covers all SPNE. But, SPNE set doesnt cover all NE</p>

CC BY-SA 4.0
2022-11-17T10:10:50.667Z
Are you asking if the negation of the statement "*all x are y*" is "*there is at least one y that is not x*"?
Giskard
CC BY-SA 4.0
2022-11-17T10:39:19.953Z
What does "(Out, price war) is only SPNE" mean here? If you mean it "is only a SPNE, but not a NE", then this is wrong, since every SPNE is a NE. If you mean it "is the only SPNE in this game", then you contradict the next sentence in which you claim that (in, accommodate) is also a SPNE...
VARulle
CC BY-SA 4.0
2022-11-17T10:47:01.320Z
@VARulle this is my inadequacy in language skill. So sorry. (Out, price war) is not SPNE, but NE. (In, accomodate) is NE and SPNE. So, NE set covers all SPNE. But, SPNE set doesnt cover all NE. Right now, my example is true?
studentp
CC BY-SA 4.0
2022-11-17T11:11:25.217Z
Yes, apart from the "typo" in the lower right corner.
VARulle
CC BY-SA 4.0
2022-11-17T11:47:16.720Z
Please link to other versions when crossposting: https://math.stackexchange.com/questions/4578612/every-nash-equilibrium-is-subgame-perfect-nash-equilibrium
Michael Greinecker
<microeconomics><game-theory><self-study><nash-equilibrium>
Every Nash equilibrium is Subgame perfect Nash equilibrium
studentp
# Every Nash equilibrium is Subgame perfect Nash equilibrium

(Asked by: username_0 on 2022-11-17)

> Every Nash equilibrium is Subgame perfect Nash equilibrium.

This statement is wrong. I show this by an counter example.

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

Is this example enough and good to disprove this statements?

Please share your ideas with me.

Thank you

Note: in the paper, there is typo.

(Out, price war) is not SPNE, but NE. (In, accomodate) is NE and SPNE. So, NE set covers all SPNE. But, SPNE set doesnt cover all NE

**Tags:** microeconomics, game-theory, self-study, nash-equilibrium

> **Comments:**
> **username_1**: Are you asking if the negation of the statement "*all x are y*" is "*there is at least one y that is not x*"?  
> **username_2**: What does "(Out, price war) is only SPNE" mean here? If you mean it "is only a SPNE, but not a NE", then this is wrong, since every SPNE is a NE. If you mean it "is the only SPNE in this game", then you contradict the next sentence in which you claim that (in, accommodate) is also a SPNE...  
> **username_0**: @username_2 this is my inadequacy in language skill. So sorry. (Out, price war) is not SPNE, but NE. (In, accomodate) is NE and SPNE. So, NE set covers all SPNE. But, SPNE set doesnt cover all NE. Right now, my example is true?  
> **username_2**: Yes, apart from the "typo" in the lower right corner.  
> **username_3**: Please link to other versions when crossposting: https://math.stackexchange.com/questions/4578612/every-nash-equilibrium-is-subgame-perfect-nash-equilibrium  

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## 0 answers

