If you advertise and your rival advertises, you each will earn $3 million in profits. If neither of you advertises, you will each earn $7 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $10 million and the non-advertising firm will earn $1 million. If you and your rival plan to be in business for 15 years, then the Nash equilibrium is for:

Nash equilibrium a concept in game theory which describes the optimal strategy for a party in a non co-operative game. It is the best strategy for the player regardless of what the other player is playing.

In this question, if both parties advertise, they earn $3 million .

If one of you advertises and the other does not, the firm that advertises will earn $10 million and the non-advertising firm will earn $1 million

If neither of you advertises, you will each earn $7 million in profits.

The profits from advertising can either be 3 million or 10 million while the profit from not advertising can either be 7 million or 1 million.

We can see the gains from advertising is more than the gain of not advertising. So the bash equilibrium is to advertise.

Please check the attached image for a table showing this game

I hope my answer helps you