<p>The example and phrasing provided by corporatefinanceinstitute.com is quite confusing.</p>
<p><strong>The definition</strong> <br>
A strategy profile is a Nash-equilibrium if no player gains by unilaterally deviating.</p>
<p>This is essentially the same as your quote:</p>
<blockquote>
<p>Under the Nash equilibrium, a player does not gain anything from deviating from their initially chosen strategy, assuming the other players also keep their strategies unchanged.</p>
</blockquote>
<p>This is true of the strategy profile (Advertise, Advertise) in the example, no one would gain by unilaterally deviating/changing their strategy.</p>
<p>However you are also correct to point out that in this case they are better off when advertising <em>no matter what</em>. The technical term is: Advertise is a <strong>strictly dominant strategy</strong>. When all players play a strictly dominant strategy we call that a <strong>strictly dominant equilibrium</strong>. All strictly dominant equilibra are also Nash-equilibria.</p>

CC BY-SA 4.0
2021-10-06T10:32:34.367Z
2021-10-06T10:32:34.367Z
Giskard
<p>From reading an answer of @Giskard <a href="https://economics.stackexchange.com/questions/47826/why-do-large-players-suffer-more-for-complete-finking-in-tit-for-tat-strategy">here</a>, I caught the word &quot;Nash equilibrium&quot;. I found <a href="https://corporatefinanceinstitute.com/resources/knowledge/economics/nash-equilibrium-game-theory/" rel="nofollow noreferrer">this link</a> quite easy to understand. This link documented:</p>
<blockquote>
<p>Under the Nash equilibrium, a player does not gain anything from
deviating from their initially chosen strategy, <strong>assuming the other
players also keep their strategies unchanged</strong>.</p>
</blockquote>
<p>While the link also has an example</p>
<blockquote>
<p>Imagine two competing companies: Company A and Company B. Both
companies want to determine whether they should launch a new
advertising campaign for their products. If both companies start
advertising, each company will attract 100 new customers. If only one
company decides to advertise, it will attract 200 new customers, while
the other company will not attract any new customers. If both
companies decide not to advertise, neither company will engage new
customers. The payoff table is below:
<a href="https://i.sstatic.net/Cbj0p.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Cbj0p.png" alt="enter image description here" /></a></p>
<p>Company A should advertise its products because the strategy provides
a better payoff than the option of not advertising. The same situation
exists for Company B. Thus, the scenario when both companies advertise
their products is a Nash equilibrium.</p>
</blockquote>
<p>It is clearly that if company A keep their initial strategy (advertising products), they will benefits regardless the decision of company B. But why in the definition, they said <strong>assuming the other players also keep their strategies unchanged</strong>? from my understanding, the company A can get benefit by keep advertising and do not care the action of company B.</p>

CC BY-SA 4.0
2021-10-06T10:26:04.703Z
Your question that I answered linked to [here](https://www.pbs.org/wgbh/americanexperience/features/nash-game/), where the phrase Nash-equilibrium appears in the second paragraph? *"If Nash got a dollar for every time someone wrote or said 'Nash equilibrium,'" Dixit has said, "he would be a rich man."* It is also a pretty basic concept of game theory, so you might benefit from reading an intro textbook.
Giskard
CC BY-SA 4.0
2021-10-06T10:30:38.933Z
Thanks a lot for your helps ,@Giskard. I am learning and I prefer to learn from the websites (that I may be able to link and search relevant information needed). And by doing that, it is my luck to have you guys experts here help me a lot. Many thanks and warmest regards again
Nguyen Lis
CC BY-SA 4.0
2021-10-06T10:33:16.080Z
You can read an e-book, that is also searchable? And it is quite common here to refer to part of a book in a question.
Giskard
<game-theory>
Clarifying the Nash equilibrium example
Nguyen Lis
# Clarifying the Nash equilibrium example

(Asked by: username_0 on 2021-10-06)

From reading an answer of @Giskard [here](https://economics.stackexchange.com/questions/47826/why-do-large-players-suffer-more-for-complete-finking-in-tit-for-tat-strategy), I caught the word "Nash equilibrium". I found [this link](https://corporatefinanceinstitute.com/resources/knowledge/economics/nash-equilibrium-game-theory/) quite easy to understand. This link documented:

> Under the Nash equilibrium, a player does not gain anything from
> deviating from their initially chosen strategy, **assuming the other
> players also keep their strategies unchanged**.

While the link also has an example

> Imagine two competing companies: Company A and Company B. Both
> companies want to determine whether they should launch a new
> advertising campaign for their products. If both companies start
> advertising, each company will attract 100 new customers. If only one
> company decides to advertise, it will attract 200 new customers, while
> the other company will not attract any new customers. If both
> companies decide not to advertise, neither company will engage new
> customers. The payoff table is below:
> [![enter image description here](https://i.sstatic.net/Cbj0p.png)](https://i.sstatic.net/Cbj0p.png)
>
> Company A should advertise its products because the strategy provides
> a better payoff than the option of not advertising. The same situation
> exists for Company B. Thus, the scenario when both companies advertise
> their products is a Nash equilibrium.

It is clearly that if company A keep their initial strategy (advertising products), they will benefits regardless the decision of company B. But why in the definition, they said **assuming the other players also keep their strategies unchanged**? from my understanding, the company A can get benefit by keep advertising and do not care the action of company B.

**Tags:** game-theory
> **Comments:**
> **username_1**: Your question that I answered linked to [here](https://www.pbs.org/wgbh/americanexperience/features/nash-game/), where the phrase Nash-equilibrium appears in the second paragraph? *"If Nash got a dollar for every time someone wrote or said 'Nash equilibrium,'" Dixit has said, "he would be a rich man."* It is also a pretty basic concept of game theory, so you might benefit from reading an intro textbook.  
> **username_0**: Thanks a lot for your helps ,@Giskard. I am learning and I prefer to learn from the websites (that I may be able to link and search relevant information needed). And by doing that, it is my luck to have you guys experts here help me a lot. Many thanks and warmest regards again  
> **username_1**: You can read an e-book, that is also searchable? And it is quite common here to refer to part of a book in a question.  

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## 1 answers

### Answer by username_1 on 2021-10-06. Score: 1 | Accepted answer

The example and phrasing provided by corporatefinanceinstitute.com is quite confusing.

**The definition**   
A strategy profile is a Nash-equilibrium if no player gains by unilaterally deviating.

This is essentially the same as your quote:

> Under the Nash equilibrium, a player does not gain anything from deviating from their initially chosen strategy, assuming the other players also keep their strategies unchanged.

This is true of the strategy profile (Advertise, Advertise) in the example, no one would gain by unilaterally deviating/changing their strategy.

However you are also correct to point out that in this case they are better off when advertising *no matter what*. The technical term is: Advertise is a **strictly dominant strategy**. When all players play a strictly dominant strategy we call that a **strictly dominant equilibrium**. All strictly dominant equilibra are also Nash-equilibria.


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