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Nash equilibrium is a state in a game where both parties have reached the optimum outcome, and trying to deviate from the existing strategy is not going to do you any good. Once you reach this state, your best option is to stay on this course.



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In a non-cooperative game, where both parties want what is best for themselves, and they don’t care what the other party gets.

But, even if it is non-cooperative, there will come a point where both of the parties are going to be an optimum position. Both of them are doing good, and any move from any party is not going to do them any good. Rather, it will worsen the situation.

So, once you get to the position, you don’t need to do anything.

And, when you start the game, your goal should be to get to that position.

For example, you are a pen manufacturer operating in a certain area. There is only one competitor in that area. And, you are currently producing 100 pens every month. And your competitor is also producing 100 pens every month. By selling them at 5 dollars each, you can make 200 dollars profit. And you have found out that your opponent is also selling the pens at the same rate and making the same profit.

At this stage, you can find out that by producing 200 pens, your cost is going to go down and you can sell each pen at 4.5 dollars and make 500 dollars in profit. In this case, it might seem like doing that will be better for you.

But, you have to realize that you have a competitor that is capable of doing the exact same thing. And when they do that, your profit will go down to 150 dollars. So, you will be worse off than before. And who is to say that your opponent is not going to start charging their pens at 4 dollars only. Then are you going to keep producing more and charge less and less. No

That would not be the best outcome.

So, according to game theory. The point where both of the companies are making 200 dollars profit by producing 100 pens is the point of nash equilibrium and any farther steps from that position is not going to help any players in the game.

So, that point will be the nash equilibrium.

Stag Hunt: It is another classic example in game theory, and instead of making a different video on stag hunt, I would like to talk about it in this context, that is, the context of nash equilibrium.

Here is the main idea of this game.

You are a hunter. You are going to hunt in a small field with another hunter. In this field on this specific day, there is one stag, and there are some rabbits. And you have no way of communicating with the other hunter.

The thing is, if you want to go for the stag alone, you will not be able to catch it. that is a two person job. So, you will need to cooperate with the other hunter in order to catch the stag.

And if you want to go for rabbits, you can catch them by yourself.

Hunting the stag together is going to give each of you three days worth of food.

The rabbits present is going to be enough for two days worth of foods.

So, if you go for the stag with the other person, both of you get three days worth of food.

If you go for stag and the other goes for rabbits, you will get nothing and the other person will get two days worth of food.

If you go for rabbits and the other person goes for the stag, you will get two days worth of foods and he other will have nothing.

If both of you go for the rabbits, both of you will get one day worth of food.

There can be multiple Nash equilibria in one game.


In the stag hunt game, both the stag/stag scenario and the rabbit/rabbit scenario are Nash equilibrium.


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Timestamps:

Intro - 0:0
Nash Equilibrium - 0:38
Example - 1:30
Stag Hunt Example - 4:13
Bonus - 9:00
Outro - 9:30