Consider the following information for a simultaneous move game: If you advertise and your rival advertises, you each will earn $5 million in profits. If neither of you advertises, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $15 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 each firm to not advertise until the rival does, and then to advertise forever.