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 hand your business down to your children,and this "bequest" goes on forever,then a Nash equilibrium when the interest rate is zero is for:
A) your firm to never advertise.
B) your firm to always advertise when your rival does, provided that the interest rate is sufficiently large.
C) each firm to not advertise until the rival does, and then to advertise forever provided the interest rate is sufficiently low.
D) each firm to advertise until the rival does not advertise, and then not advertise forever.

Question

Quizplus · Accepted Answer

In a Nash equilibrium, neither player has an incentive to change their strategy given the other player's strategy. 
If one firm advertises and the other does not, the advertising firm earns $10 million and the non-advertising firm only earns $1 million. Therefore, if both firms advertise, they both earn $3 million in profits, which is less than if neither firm advertises and they each earn $7 million in profits. 
However, if one firm starts advertising, the other firm will have an incentive to start advertising as well to earn more profits. Therefore, if the interest rate is sufficiently low, it is optimal for each firm to wait until the other firm starts advertising and then both firms should advertise forever. This leads to an equilibrium in which both firms advertise forever and earn $3 million in profits each.

If You Advertise and Your Rival Advertises,you Each Will Earn