Microeconomics: Principles & Policy
14th Edition
ISBN: 9781337794992
Author: William J. Baumol, Alan S. Blinder, John L. Solow
Publisher: Cengage Learning
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Students have asked these similar questions
Rock-paper-scissors is a game in which players typically use mixed strategies. Can you think of other examples? What are some of the characteristics of games that usually involve playing mixed strategies?
In dynamic game theory, a situation where a player is using non-credible threat is an examples of subgame perfect Nash equilibrium, explain why or why not?
Consider the following payoff matrix that is below :
A. Does Player A have a dominant startegy? Explain why or why not
b. Does player B have a dominant strategy? Explain why or why not.
Player B Strategy
1
2
Player A Strategy
1
$2,000 \ $1,000
-$1,000 \ -$2,000
2
-$2,000 \ -$1,000
$1,000 \ $2,000
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In which game does the US get a better outcome? Why? In the real world, what could the US do to make this outcome more likely?
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The order of play tends to matter in sequential games where rivals must predict best reply-responses and counter-responses in order to achieve a desired payoff. Discuss an instance in which you or your firm used game theory and explain why the relationship between the players was a strategic one. Did the use of a credible threat or commitment affect the outcome? Were there any first-mover of fast-second strategies used?
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Consider the following dynamic game. There are two players (P1, P2). Player 2 tries to rob Player 1. If Player 1 pays $100, the game is over with Player 1 (victim) paying $100 to Player 2 (robber) (P1: -$100, P2: +$100). If Player 1 refuses to pay $100, then Player 2 has two choices: one is to hurt Player 1 (P1: -$5,000, P2: -$1,000) and the other is to walk away (P1: 0, P2: 0). Explain how to find an equilibrium in this game.
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Is life a non-zero sum game?
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Construct a game-theory matrix involving two firms and their decisions on high versus low advertising budgets and the effects of each on profits. Show a circumstance in which both firms select high advertising budgets even though both would be more profitable with low advertising budgets. Why won’t they unilaterally cut their advertising budgets?
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Explain why the value of a matrix game is positive if all of the payoffs are positive.
A. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c)will be negative and ad−bcwill be negative. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the payoffs are positive, the saddle value will also be positive. Thus, the value, v, is positive.
B. If the matrix game is strictly determined and all of the payoffs are positive, the saddle value will be negative. Thus, the value, v, is positive. If the matrix game is nonstrictly determined, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive.
C. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the…
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Describe the fundamental contribution of game theory?
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Consider a game where player A moves first, choosing between Left and Right. Then, after observing player A’s choice, player B moves next choosing between Up and Down. Which of the following is true?
This is a game where players A and B have the same number of strategies.
Player A will get a higher payoff than player B as A moves first.
This is game will only have one Nash equilibrium.
This is a game of perfect information.
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In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill.
Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A.
Is there a pure strategy? Why or why not?
Determine the optimal strategies and the value of this game. Does the game favor one player over the other?
Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.
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