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PROBLEM SET #7 Multiple Choice Questions 1. 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 advertise, 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 be in business for only one year, the Nash equilibrium is A. For each firm to advertise B. For neither firm to advertise C. For your firm to advertise and the other not to advertise D. None of the statements associated with this question are correct 2. If you advertise and your rival advertises, you each will earn $4 million in profits. If neither of you advertise, 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 A. For each firm to advertise every year B. For neither firm to advertise in early years, but to advertise in later years C. For each firm to not advertise in any year D. For each firm to advertise in early years, but not advertise in later years Questions 3-5 are based on the following game, where firms one and two must independently decide whether to charge high or low prices. 3. Which of the following are Nash equilibrium payoffs in the one-shot game? A. (0, 0) B. (5, -5) C. (-5, 5) D. (10, 10) 4. Which of the following are the Nash equilibrium payoffs (each period) if the game is repeated 10 times? A. (0, 0) B. (5, -5) C. (-5, 5) D. (10, 10) 5. Suppose the game is infinitely repeated. Then the "best" the firms could do in a Nash equilibrium is to earn per period. A. (0, 0) B. (5, -5) C. (-5, 5) D. (10, 10) 6. 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 Nash equilibrium strategies? A. (Enter, hard) and (not enter, hard) B. (Enter, soft) and (not enter, soft) C. (Not enter, hard) and (enter, soft) D. (Enter, hard) and (not enter, soft) Answer questions 7-10 based on the following information for a one-shot game: 7. What are dominant strategies for Firm A and Firm B respectively? A. (Low price, high price) B. (High price, low price) C. (High price, high price) D. (Low price, low price) 8. What are secure strategies for firm A and firm B respectively? A. (Low price, high price) B. (High price, low price) C. (High price, high price) D. (Low price, low price) 9. What are the Nash equilibrium strategies for firm A and B respectively? A. (Low price, high price) B. (High price, low price) C. (High price, high price) D. (Low price, low price) 10. If this one-shot game is repeated 100 times, the Nash-equilibrium payoffs of the players will be ________________ each period. A. (2, 2) B. (10, -8) C. (-8, 10) D. (6, 6) 11. Which of the following are important determinants of collusion in pricing games? A. The number of firms B. Firm size C. History D. All of the statements associated with this question are correct 12. Which of the following is true? A. In a one-shot game, a collusive strategy always represents a Nash equilibrium B. A perfect equilibrium occurs when each player is doing the best he can regardless of what the other player is doing C. Each Nash equilibrium is a perfect equilibrium D. Every perfect equilibrium is a Nash equilibrium 13. Which of the following is true? A. For a finitely repeated game, the game is played enough times to effectively punish cheaters and therefore collusion is likely B. In an infinitely repeated game with a low interest rate, collusion is unlikely because the game unravels so that effective punishment cannot be used during any time period C. A secure strategy is the optimal strategy for a player no matter what the opponent does D. None of the statements associated with this question are correct 14. Collusion is: A. Legal in the United States B. Not possible when firms interact repeatedly forever C. More likely in industries with a large number of firms D. None of the statements associated with this question are correct 14. Which of the following conditions are necessary for the existence of a Nash equilibrium? A. The existence of dominant strategies for both players B. The existence of a dominant strategy for one player and the existence of secure strategy for another player C. The existence of secure strategy for both players D. None of the statements associated with this question are correct 15. Which of the following is true for a Nash equilibrium of a two-player game? A. The joint payoffs of the two players are highest compared to other strategy pairs B. Given another player's strategy stipulated in that Nash equilibrium, a player cannot improve his welfare by changing his strategy C. A Nash equilibrium is always unique in real world problems D. Given another player's strategy stipulated in that Nash equilibrium, a player cannot improve his welfare by changing his strategy and a Nash equilibrium is always unique in real world problems 16. Game theory is especially useful for analysis in the following types of markets: A. Perfect competition B. Monopolistic competition C. Oligopoly D. Monopoly Use the following information to answer questions 17-18: Suppose that you are a manager. You are considering whether or not to monitor employees with the payoffs in the following normal form game. 17. Which of the following pair of strategies constitute a Nash equilibrium? A. Manager monitors and worker works B. Manager does not monitor and worker works C. Manager monitors and worker shirks D. None of the statements associated with this question are correct 18. What should the manager do to solve the shirking problem? A. Always monitor B. Never monitor C. Sincerely tell workers not to shirk D. Engage in "random" spot checks of the work place 19. Which of the following is true? A. A Nash equilibrium is always perfect B. A perfect equilibrium is always Nash C. A Nash equilibrium is always perfect in a multistage game D. Perfect equilibrium and Nash equilibrium are the same concept but with different names Refer to the following normal form game of price competition for questions 20-22. 20. Suppose the game is infinitely repeated, and the interest rate is 10%. Both firms agree to charge a high price, provided no player has charged in low price in the past. If both firms stick to this agreement, then the present value of Firm A's payoffs are: A. 220 B. 110 C. 330 D. 550 21.Suppose that Firm A deviates from a trigger strategy to support a high price. What is the present value of A's payoff from cheating? A. 70 B. 50 C. 30 D. 20 22. What is the maximum interest rate that can sustain collusion? A. 30% B. 15% C. 66.7% D. 20% 23. It is easier to sustain tacit collusion in an infinitely repeated game if: A. The present value of cheating is higher B. There are more players in the game C. The interest rate is lower D. The present value of cheating is higher and the interest rate is lower 24. When a worker announces that he plans to quit, say next month, the "threat" of being fired has no bite. The worker may find it in his interest to shirk. What can the manager do to overcome this problem? A. "Fire" the worker as soon as he announces his plans to quit B. Provide the worker some rewards for good work that extend beyond the termination of employment with your firm C. Monitor the worker more frequently than usual and fire him when he is caught shirking D. Pay the worker some rewards when he announces his plan to quit 25. A finitely repeated game differs from an infinitely repeated game in that: A. The former needs a lower interest rate to support collusion than the latter needs B. There is an "end-of-period" problem for the former C. A collusive outcome can usually be sustained in the former but not the latter D. All of the statements associated with this question are correct 26. A coordination problem arises whenever there: A. Is no Nash equilibrium in a game B. Is a unique Nash equilibrium but it is not very desirable C. Are multiple Nash equilibriam D. Are no dominant strategies for both players 27. Which of the following is not true? A. An extensive form representation usually provides more information than a normal form representation of a game B. A normal form game is most useful for sequential-move games C. The notion of perfect equilibrium is more useful in analyzing extensive form games than normal form games D. The notion of credible threats makes more sense in extensive form representations than in normal form representations of a game 28. A Nash equilibrium with a non-credible threat as a component is: A. A perfect equilibrium B. Not a perfect equilibrium C. A sequential equilibrium D. A somewhat perfect equilibrium 29. Which of the following is a valid critique of the use of game theory in economics? A. Payoffs to players may be difficult to measure B. Players may not have complete information about each other's payoffs C. Game theory assumes rational players D. All of the statements associated with this question are correct Refer to the following normal form game of price competition for questions 30-31. 30. Firm B is the incumbent facing potential entry from its rival; Firm A. Firm A's strategies consist of {Entry, Stay Out}. Firm B's strategies are then {hard if entry; hard if stay out; soft if entry; soft if stay out}. Find the subgame Nash equilibrium to this game, if one exists. A. Firm A plays {Stay Out}; Firm B plays {Hard if Entry} B. Firm A plays {Entry}; Firm B plays {Hard if Entry} C. Firm A plays {Entry}; Firm B plays {Soft if Entry} D. There is no subgame Nash equilibrium to this game 31. Firm B is the incumbent facing potential entry from its rival; Firm A. Firm A's strategies consist of {Entry, Stay Out}. Firm B's strategies are then {hard if entry; hard if stay out; soft if entry; soft if stay out}. Find the non-subgame Nash equilibrium to this game, if one exists. A. Firm A plays {Stay Out}; Firm B plays {Hard if Entry} B. Firm A plays {Entry}; Firm B plays {Hard if Entry} C. Firm A plays {Entry}; Firm B plays {Soft if Entry} D. There is no non-subgame Nash equilibrium to this game