Both firms would prefer the outcome where each spends the mutually efficient amount, over the outcome...

 

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Both firms would prefer the outcome where each spends the mutually efficient amount, over the outcome where each spends the Nash equilibrium amount. Suppose that they try to sustain mutually efficient behavior by means of the following grim trigger strategy: In the first month, each firm spends the mutually efficient amount on advertising. In future months, so long as they both remain in business, each will continue to spend the mutually efficient amount so long as the other continues to do so. But if its rival ever spends more (or less) than the mutually efficient amount, then in all future periods, a firm will spend the Nash equilibrium amount on advertis- ing. If both firms use this strategy, how much will each spend per month on adver- tising while both are in business? What will be their monthly profit? If 8 = .9, what will be the expected total profits of each firm over the time they remain in business? Suppose that Firm 2 is playing the grim strategy described above. How much profit could Firm 1 make in the first month by choosing the amount of advertising that maximizes her profit in the first month? If she does this, how much profit could she make in later months? Explain your answer. Both firms would prefer the outcome where each spends the mutually efficient amount, over the outcome where each spends the Nash equilibrium amount. Suppose that they try to sustain mutually efficient behavior by means of the following grim trigger strategy: In the first month, each firm spends the mutually efficient amount on advertising. In future months, so long as they both remain in business, each will continue to spend the mutually efficient amount so long as the other continues to do so. But if its rival ever spends more (or less) than the mutually efficient amount, then in all future periods, a firm will spend the Nash equilibrium amount on advertis- ing. If both firms use this strategy, how much will each spend per month on adver- tising while both are in business? What will be their monthly profit? If 8 = .9, what will be the expected total profits of each firm over the time they remain in business? Suppose that Firm 2 is playing the grim strategy described above. How much profit could Firm 1 make in the first month by choosing the amount of advertising that maximizes her profit in the first month? If she does this, how much profit could she make in later months? Explain your answer.

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