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From reading an answer of @Giskard here, I caught the word "Nash equilibrium". I found this link 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

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.

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    $\begingroup$ Your question that I answered linked to here, 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. $\endgroup$
    – Giskard
    Oct 6, 2021 at 10:26
  • $\begingroup$ 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 $\endgroup$
    – Nguyen Lis
    Oct 6, 2021 at 10:30
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    $\begingroup$ 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. $\endgroup$
    – Giskard
    Oct 6, 2021 at 10:33

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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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