Two rival firms compete in the same market. Advertising by one firm increases its demand, but takes some business away from the other. In any month, the profits of each of the two firms depends on how much it spends on advertising and on how much the other firm spends. When Firm 1 spends x and Firm 2 spends x2 on advertising in a given month, profits in that month for Firm 1 will be 1 T (x1, x) = 40x and for Firm 2, profits will be 20x2, T2(x, x2) = 40x21x2 - 20x1. They plan to play this game for the indefinite future, but there is always a chance that their market will disappear. In particular, after any month, we suppose that the probability that they are both in business in the next month is 6, where 0 < d < 1. Since the probability that they are both in business t months later must be dt, profits t months into the future are discounted by St. A) If Firm 1 uses the tit-for-tat strategy, amd Firm 2 uses the cheat-and- earn-forgiveness strategy, What will Firm 2's profits be in the first month. If both firms are still in operation in the second month, what will Firm 2's. profits be in that month? If both firms are still in operation, what will Firm 2's profits be in the third and later months. B) If Firm 1 uses the tit-for-tat strategy and Firm 2 uses the cheat-and- earn-forgiveness strategy, for what values of 6 will Firm 2 have a greater payoff from using the tit-for-tat strategy rather than the cheat-and-earn-forgiveness strategy?