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.

Perfect.

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?

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.

thank you so much!