<p>Consider the following game between P1 (row player) and P2 (column player):</p>
<p><span class="math-container">\begin{array}{|c|c|c|}\hline
&amp; L &amp; R \\\hline
T&amp; 1,1 &amp; 2,0 \\\hline
B&amp; 0,0 &amp; 1,1 \\\hline
\end{array}</span></p>
<ul>
<li><span class="math-container">$T$</span> is P1's dominant strategy</li>
<li><span class="math-container">$T$</span> is P1's best response to both of P2's strategies <span class="math-container">$L$</span> and <span class="math-container">$R$</span></li>
<li><span class="math-container">$L$</span> is P2's best response to P1's strategy <span class="math-container">$T$</span></li>
<li><span class="math-container">$R$</span> is P2's best response to P1's strategy <span class="math-container">$B$</span></li>
<li><span class="math-container">$(T,L)$</span> is the only Nash equilibrium</li>
</ul>
<p>Generalizing from the above observations:</p>
<ol>
<li>A strategy is dominant if and only if it is a best response to each of the other player's strategies, e.g. P1's <span class="math-container">$T$</span>.</li>
<li>A strategy that is a best response to some but not all of the other player's strategies cannot be a dominant strategy, e.g. P2's <span class="math-container">$L$</span> and <span class="math-container">$R$</span>.</li>
<li>A Nash equilibrium is a pair of mutually best responding strategies, e.g. <span class="math-container">$(T,L)$</span>.</li>
</ol>

CC BY-SA 4.0
2021-03-31T02:20:56.197Z
2021-03-31T02:20:56.197Z
Herr K.
<p>I can't seem to get the differences of these terms.</p>
<p>I watched <a href="https://youtu.be/VuDutyTs_r8?t=137" rel="nofollow noreferrer">this video</a> that has the differences of <strong>best response</strong> and <strong>Nash equilibrium</strong>:
<a href="https://i.sstatic.net/1Iiui.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1Iiui.png" alt="best response vs Nash equilibrium" /></a></p>
<p>But then I heard about <strong>dominant strategies</strong> from another video and searched for differences to land at this <a href="https://quizlet.com/279580670/ch-13-econ-micro-flash-cards/#:%7E:text=Is%20a%E2%80%8B%20player%27s%20best,not%20always%20a%20dominant%20strategy." rel="nofollow noreferrer">quiz question</a>:</p>
<blockquote>
<p>Is a​ player's best response in a game the same as his dominant​ strategy?
Not necessarily. If a player has a dominant​ strategy, then it is his best​ response; however, every best response is not always a dominant strategy.</p>
</blockquote>
<p>Is there a table form that shows the differences of these 3 based on a specific player and what other players would do?</p>

<game-theory><nash-equilibrium><dominant-strategy>
Differences between best response, dominant strategy and Nash equilibrium
heretoinfinity
# Differences between best response, dominant strategy and Nash equilibrium

(Asked by: username_0 on 2021-03-30)

I can't seem to get the differences of these terms.

I watched [this video](https://youtu.be/VuDutyTs_r8?t=137) that has the differences of **best response** and **Nash equilibrium**:
[![best response vs Nash equilibrium](https://i.sstatic.net/1Iiui.png)](https://i.sstatic.net/1Iiui.png)

But then I heard about **dominant strategies** from another video and searched for differences to land at this [quiz question](https://quizlet.com/279580670/ch-13-econ-micro-flash-cards/#:%7E:text=Is%20a%E2%80%8B%20player%27s%20best,not%20always%20a%20dominant%20strategy.):

> Is a​ player's best response in a game the same as his dominant​ strategy?
> Not necessarily. If a player has a dominant​ strategy, then it is his best​ response; however, every best response is not always a dominant strategy.

Is there a table form that shows the differences of these 3 based on a specific player and what other players would do?

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

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## 1 answers

### Answer by username_1 on 2021-03-31. Score: 3

Consider the following game between P1 (row player) and P2 (column player):

\begin{array}{|c|c|c|}\hline
& L & R \\\hline
T& 1,1 & 2,0 \\\hline
B& 0,0 & 1,1 \\\hline
\end{array}

* $T$ is P1's dominant strategy
* $T$ is P1's best response to both of P2's strategies $L$ and $R$
* $L$ is P2's best response to P1's strategy $T$
* $R$ is P2's best response to P1's strategy $B$
* $(T,L)$ is the only Nash equilibrium

Generalizing from the above observations:

1. A strategy is dominant if and only if it is a best response to each of the other player's strategies, e.g. P1's $T$.
2. A strategy that is a best response to some but not all of the other player's strategies cannot be a dominant strategy, e.g. P2's $L$ and $R$.
3. A Nash equilibrium is a pair of mutually best responding strategies, e.g. $(T,L)$.


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