Exam 10: Game Theory: Inside Oligopoly

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Refer to the normal-form game of price competition shown below. Refer to the normal-form game of price competition shown below.   For what values of x is strategy D strictly dominant for firm B? For what values of x is strategy D strictly dominant for firm B?

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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?

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Which of the following is a correct statement?

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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:

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Consider the following innovation game: Firm A must decide whether or not to introduce a new product. Firm B must decide whether or not to clone firm A's product. If firm A introduces and B clones, then firm A earns $2 and B earns $15. If A introduces and B does not clone, then A earns $8 and B earns $1. If firm A does not introduce, both firms earn profits of 0. Which of the following is true?

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Game theory suggests that, in the absence of patents, the privately motivated innovation decisions of firms might lead to:

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Which of the following is true for a Nash equilibrium of a two-player game?

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If you advertise and your rival advertises, you each will earn $3 million in profits. If neither of you advertises, you will each earn $7 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $10 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:

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According to various trade publications, over 200,000 changes are made in airfares each day. Why do you think this is the case?

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In the game shown below, firms 1 and 2 must independently decide whether to charge high or low prices. In the game shown below, firms 1 and 2 must independently decide whether to charge high or low prices.   Which of the following are the Nash equilibrium payoffs (each period) if the game is repeated 10 times? Which of the following are the Nash equilibrium payoffs (each period) if the game is repeated 10 times?

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Refer to the normal-form game of price competition in the payoff matrix below. Refer to the normal-form game of price competition in the payoff matrix below.   What is the maximum interest rate that can sustain collusion? What is the maximum interest rate that can sustain collusion?

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In the game depicted below, firms 1 and 2 must independently decide whether to charge high or low prices. In the game depicted below, firms 1 and 2 must independently decide whether to charge high or low prices.   Which of the following are secure strategies for players 1 and 2, respectively? Which of the following are secure strategies for players 1 and 2, respectively?

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Refer to the normal-form game of bargaining shown below. Refer to the normal-form game of bargaining shown below.   Suppose that management and the union are bargaining over how much of a $500 surplus to give to the union. It is assumed that the surplus can only be split into $250 increments. Furthermore, negotiations are set up such that management and the union must simultaneously and independently write down the amount of surplus to allocate to the union. The payoff structure to this one-shot bargaining game is listed in Figure 10-16. The number of efficient outcomes resulting from the bargaining game is: Suppose that management and the union are bargaining over how much of a $500 surplus to give to the union. It is assumed that the surplus can only be split into $250 increments. Furthermore, negotiations are set up such that management and the union must simultaneously and independently write down the amount of surplus to allocate to the union. The payoff structure to this one-shot bargaining game is listed in Figure 10-16. The number of efficient outcomes resulting from the bargaining game is:

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According to a spokesperson for cereal maker Kellogg, "… for the past several years, our individual company growth has come out of the other fellow's hide." a. What implications does this statement have for the level of advertising in the cereal industry? b. Using the following hypothetical payoff matrix, explain how trigger strategies can be used to support the collusive level of advertising in an infinitely repeated game. For what values of the interest can collusion be sustained?

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There are two existing firms in the market for computer chips. Firm A knows how to reduce the production costs for the chip and is considering whether to adopt the innovation or not. Innovation incurs a fixed setup cost of C, while increasing the revenue. However, once the new technology is adopted, another firm, B, can adopt it with a smaller setup cost of C/3. If A innovates and B does not, A earns $30 in revenue while B earns $10. If A innovates and B does likewise, both firms earn $20 in revenue. If neither firm innovates, both earn $10. Under what condition will firm A innovate?

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If you advertise and your rival advertises, you each will earn $4 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 $1 million and the non-advertising firm will earn $5 million. If you and your rival plan to be in business for 10 years, then the Nash equilibrium is:

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When analyzing the behavior of oligopolists, which of the following is crucial for the success of game theoretic analysis?

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Refer to the normal-form game of price competition shown below. Refer to the normal-form game of price competition shown below.   For what values of x is strategy (B, D) the only Nash equilibrium of the game? For what values of x is strategy (B, D) the only Nash equilibrium of the game?

(Multiple Choice)
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If you advertise and your rival advertises, you each will earn $4 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 $1 million and the non-advertising firm will earn $5 million. Suppose this game is repeated for a finite number of times, but the players do not know the exact date at which the game will end. The players can earn profits of $10 each period as a Nash equilibrium to a repeated play of the game if the probability the game terminates at the end of any period is:

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If you advertise and your rival advertises, you each will earn $4 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 $1 million and the non-advertising firm will earn $5 million. Which of the following is true?

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