Subject: Manegerial economic & policy Q#1) In your answer to each part below, include references to specific games discussed in the chapter as appropriate. a. If a game has a dominant strategy equilibrium, does it have a Nash equilibrium? b. If a game has a Nash equilibrium, does it have a dominant strategy equilibrium? c. If one firm has a dominant strategy, can another firm take advantage of that fact in deciding on its optimal strategy? d. Can a game have more than one dominant strategy equilibrium? Can a game have more than one Nash equilibrium?

Subject: Manegerial economic & policy Q#1) In your answer to each part below, include references to specific games discussed in the chapter as appropriate. a. If a game has a dominant strategy equilibrium, does it have a Nash equilibrium? b. If a game has a Nash equilibrium, does it have a dominant strategy equilibrium? c. If one firm has a dominant strategy, can another firm take advantage of that fact in deciding on its optimal strategy? d. Can a game have more than one dominant strategy equilibrium? Can a game have more than one Nash equilibrium?

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5PA

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Game Theory a) Consider the following game represented by the game tree below. If you observe Blue Bank playing medium and Green Bank playing bottom, would you be surprised by their choices? Carefully explain why or why not. b) Now assume that Blue and Green Banks play the game with the same actions and payoffs as in a) but they make their choices simultaneously. What is the payoff matrix for this new game? What do you predict will happen in the game? Explain. c) Assume that the game from part a) is played five times, i.e. Blue and Green Banks play a repeated game with the stage game described in a). What do you predict will happen in the game? Explain.
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Suppose you manage a large company’s marketing department and are responsible for deciding whether or not to advertise in the Super Bowl. Your team of analysts estimate that for each advertisement, your firm would generate $6 million in additional revenue for the company. It cost $7 million to run a 30-second advertisement. Therefore, your company would expect to lose $1 million in profit for each advertisement. Explain why it could still be worthwhile to purchase an advertisement, even though you know in advancethat your company would lose $1.5 million in profit
Suppose you manage a large company’s marketing department and are responsible for deciding whether or not to advertise in the Super Bowl. Your team of analysts estimate that for each advertisement, your firm would generate $6 million in additional revenue for the company. It cost $7 million to run a 30-second advertisement. Therefore, your company would expect to lose $1 million in profit for each advertisement. a) Explain why it could still be worthwhile to purchase an advertisement, even though you know in advance that your company would lose $1 million in profit? b)Depict this situation with a game theory payoff matrix. Your company (A) and a major competitor (B) have two potential strategies: to advertise or to not advertise during the Super Bowl. The payoffs in each cell represent the change in firm profits from advertising. Create payoffs in each cell such that the Nash equilibrium is that both firms advertise despite having a higher profit if neither firm advertised.
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The two major scooter companies in India, ABC and XYZ, are competing for a fixed market. If both manufacturers make major model changes in a year, then their percentage market share not change. Also, if they both do not make major model changes, their percentage market share remains constant. If ABC makes a major model change and XYZ does not, then ABC is able to take away a% of the market away from XYZ, and if XYZ makes a major model change ABC does not, XYZ is able to take away b% of the market away from ABC. Express this as a 2 x 2 game and solve for the optimal strategy for each of the companies.
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12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?
Subject: Manegerial economics & policy Suppose this game is repeated indefinitely. Suppose both firms charge the high price. How can this strategy become stable in the repeated game? What if the game were only repeated for a set number of periods?
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