The next three questions are based on the following game, where firms one and two must independently decide whether to charge high or low prices.
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Firm One
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Firm Two
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High Price
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High Price
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(10, 10)
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Low Price
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(5, -5)
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1. Which of the following are Nash equilibrium payoffs in the one-shot game?
2. Which of the following are the Nash equilibrium payoffs (each period) if the game is repeated 10 times?
3. Suppose the game is infinitely repeated. Then the "best" the firms could do in a Nash equilibrium is to earn per period.
4. Consider the following entry game. Here, firm B is an existing firm in the market, and firm A is a potential entrant. Firm A must decide whether to enter the market (play "enter") or stay out of the market (play "not enter"). If firm A decides to enter the market, firm B must decide whether to engage in a price war (play "hard"), or not (play "soft"). By playing "hard", firm B ensures that firm A makes a loss of $1 million, but firm B only makes $1 million in profits. On the other hand, if firm B plays "soft", the new entrant takes half of the market, and each firm earns profits of $5 million. If firm A stays out, it earns zero while firm B earns $10 million. Which of the following are perfect equilibrium strategies?
Answer the next two questions based on the following payoff matrix:
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Firm A
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Firm B
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Low Price
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Low Price
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(10, 9)
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High Price
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(-10, 7)
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5. What are the secure strategies for Firm A and Firm B respectively?
6. Which of the following is NOT true?