<p><span class="math-container">\begin{array}{|c|c|c|}
\hline
&amp;L&amp;R\\\hline
T&amp;1,1&amp;0,0\\\hline
B&amp;0,0&amp;0,0\\\hline
\end{array}</span></p>

<p>In the game above, there are two pure strategy Nash equilibria: </p>

<ul>
<li><span class="math-container">$(T,L)$</span> is an equilibrium in weakly domi<strong>nant</strong> strategies;</li>
<li><span class="math-container">$(B,R)$</span> is an equilibrium in weakly domi<strong>nated</strong> strategies.</li>
</ul>

<p>Noting that "dominant" and "dominated" are two different words, I believe the above example answers both the question in your post as well as your question in the comment below. </p>

CC BY-SA 4.0
2019-11-21T22:08:59.327Z
This is not the question I asked. I asked about Nash equilibrium which is NOT an equilibrium in weakly dominated strategies.
Aqqqq
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2019-11-21T22:09:54.680Z
@Aqqqq Actually, this is the answer to the question you asked! You edited the question later. This is clear from the [edit history](https://economics.stackexchange.com/posts/32884/revisions).
Giskard
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2019-11-21T22:11:20.233Z
@Giskard I edited the question to make it clearer for understanding. No meaning was changed. The only thing I added was the content in the bracket.
Aqqqq
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2019-11-21T22:12:28.700Z
@Aqqqq Sorry (though I am completely right and adding contradictory information in brackets does not change this).
Giskard
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2019-11-21T22:12:36.143Z
@Aqqqq: Your question asks for NE that's not in weakly domi**nant** strategies. $(B,R)$ is NOT a Nash equilibrium in weakly domi**nant** strategies, it's in weakly domi**nated** strategies.
Herr K.
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2019-11-21T22:14:56.893Z
@Giskard Does not sound contradictory for me. I only realized after seeing this answer that this could be misunderstanding. Also did you even read the question title?
Aqqqq
CC BY-SA 4.0
2019-11-21T22:15:58.133Z
@Aqqqq I believe you. Herr K's answer does answer both your questions though.
Giskard
CC BY-SA 4.0
2019-11-21T22:06:20.127Z
2019-11-21T22:21:25.253Z
2019-11-21T22:21:25.253Z
Herr K.
<p>I know that it is possible to have a Nash equilibrium which is not an equilibrium in dominant strategy, but is it also applicable for equilibrium in weakly dominant strategy (i.e. a Nash equilibrium which is NOT an equilibrium in weakly dominant strategy)? If yes, what would be an example?</p>

<game-theory><nash-equilibrium><dominant-strategy>
Is it possible to find a nash equilibrium that is not an equilibrium in weakly dominant strategy?
Aqqqq
# Is it possible to find a nash equilibrium that is not an equilibrium in weakly dominant strategy?

(Asked by: username_0 on 2019-11-21)

I know that it is possible to have a Nash equilibrium which is not an equilibrium in dominant strategy, but is it also applicable for equilibrium in weakly dominant strategy (i.e. a Nash equilibrium which is NOT an equilibrium in weakly dominant strategy)? If yes, what would be an example?

**Tags:** game-theory, nash-equilibrium, dominant-strategy

---

## 1 answers

### Answer by username_1 on 2019-11-21. Score: 2

\begin{array}{|c|c|c|}
\hline
&L&R\\\hline
T&1,1&0,0\\\hline
B&0,0&0,0\\\hline
\end{array}

In the game above, there are two pure strategy Nash equilibria:

* $(T,L)$ is an equilibrium in weakly domi**nant** strategies;
* $(B,R)$ is an equilibrium in weakly domi**nated** strategies.

Noting that "dominant" and "dominated" are two different words, I believe the above example answers both the question in your post as well as your question in the comment below.

> **Comments:**
> **username_0**: This is not the question I asked. I asked about Nash equilibrium which is NOT an equilibrium in weakly dominated strategies.  
> **username_2**: @Aqqqq Actually, this is the answer to the question you asked! You edited the question later. This is clear from the [edit history](https://economics.stackexchange.com/posts/32884/revisions).  
> **username_0**: @Giskard I edited the question to make it clearer for understanding. No meaning was changed. The only thing I added was the content in the bracket.  
> **username_2**: @Aqqqq Sorry (though I am completely right and adding contradictory information in brackets does not change this).  
> **username_1**: @Aqqqq: Your question asks for NE that's not in weakly domi**nant** strategies. $(B,R)$ is NOT a Nash equilibrium in weakly domi**nant** strategies, it's in weakly domi**nated** strategies.  
> **username_0**: @Giskard Does not sound contradictory for me. I only realized after seeing this answer that this could be misunderstanding. Also did you even read the question title?  
> **username_2**: @Aqqqq I believe you. Herr K's answer does answer both your questions though.  

---

