EBK MICROECONOMICS
2nd Edition
ISBN: 8220103679701
Author: List
Publisher: YUZU
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Question
Chapter 13, Problem 6P
To determine
Pay-off matrix and existence of pure-strategy Nash equilibrium in a penalty kick round.
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**Practice***
Amy and Bob are playing the following board game:(I) Amy starts. She has three possible actions: Pass, Attack, or Defend.(II) Bob observes what Amy chose, and then chooses between three actions with the same names: Pass, Attack, or Defend.(III) If either player passes, or one attacks and the other defends, then the game ends. But if either both players attack, or if both players defend, then Amy has to choose between two actions: Respond or Not Respond.
The payoffs are as follows:- If both players pass, both players get a payoff of 0.- If a player attacks and the other player defends, the player that attacks gets a payoff of 1, while the player that defended gets a payoff of 2.- If a player passes but the other player attacks or defends, the player who passes gets a payoff of -1, and the player who attacked or defended gets a payoff of 3.- If both players attack or both players defend:– If Amy responds, she gets a payoff of 4, and Bob gets a payoff of 0.– If Amy does…
Two athletes of equal ability are competing for a prize of $12,000. Each is deciding whether to take a dangerous performance-enhancing drug. If one athlete takes the drug and the other does not, the one who takes the drug wins the prize. If both or neither take the drug, they tie and split the prize. Taking the drug imposes health risks that are equivalent to a loss of XX dollars.
Complete the following payoff matrix describing the decisions the athletes face. Enter Player One's payoff on the left in each situation, Player Two's on the right.
Player Two's Decision
Take Drug
Don't Take Drug
Player One's Decision
Take Drug
,
,
Don't Take Drug
,
,
True or False: The Nash equilibrium is taking the drug if X is greater than $6,000.
True
False
Suppose there was a way to make the drug safer (that is, have lower XX).
Which of the following statements are true about the effects of making the drug safer? Check all that…
Two athletes of equal ability are competing for a prize of $10,000. Each is deciding whether to take a dangerous performance enhancing drug. If one athlete takes the drug, and the other does not, the one who takes the drug wins the prize. If both or neither take the drug, they tie and split the prize. Taking the drug imposes health risks that are equivalent to a loss of X dollars.
a) Draw a 2×2 payoff matrix describing the decisions the athletes face.
b) For what X is taking the drug the Nash equilibrium?
c) Does making the drug safer (that is, lowering X) make the athletes better or worse off? Explain.
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