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You operate in a duopoly in which you and a rival must simultaneously decide what price to advertise in the weekly newspaper. If you each charge a...

4. You operate in a duopoly in which you and a rival must simultaneously decide what price to advertise in the weekly newspaper.  If you each charge a low price, you each earn zero profits.  If you each charge a high price, you each earn profits of $3.  If you charge different prices, the one charging the higher price loses $5 and the one charging the lower price makes $5.
a. Find the Nash equilibrium for a one-shot version of this game.
b. Now suppose the game is infinitely repeated.  If the interest rate is 10 percent, can you do better than you could in a one-shot play of the game?  Explain.
c. Explain how "history" affects the ability of firms in this game to achieve an outcome superior to that of the one-shot version of the game.

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