Nash equilibrium question---

the cfa answer is A, but my answer is C.
What are your answers?

What’s the definition of a Nash equilibrium?

Here is my answer why cfa answer is A (i know i’m wrong when i choose C)
to find the definition of a Nash equilibrium, we need to know the reaction of the opponents.
An in this case, for example we are Chain 1 → we guess chain 2 absolutely chooses open 24 hours —> we choose open 24 hours

What is the definition of a Nash equilibrium?

It is a game theory concept, a pair of strategies such that neither players can gain by a unilateral change of strategies.


If both chains close at 9:00 PM, can either one gain by changing to staying open 24 hours (assuming the other doesn’t change strategy); i.e., is answer C a Nash equilibrium?

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Pick any box to start.
i.e Top left.

Pick one of the parties and consider them making a decision on their own.
i.e Chain 1
They look at 180 profits.
If they move to 24 hours they make 540 so they move.

We are now in bottom left.
Look at Chain 1 profits 540.
It makes no sense to move
Look at chain 2
They make 75
Makes sense for them to move to 24 hours
Profits now 140

Now bottom right
Chain 1 - 24 hrs - profits 108.
No sense to move as profits would fall to 55
Chain 2 - 24 hrs - profits 140
No sense to move as profits would fall to 75

Each chain - think on its own assuming the other party won’t change - means we end up bottom right. But here profits are lower for both parties than top left.

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thank you so much!