MICROECONOMICS
MICROECONOMICS
11th Edition
ISBN: 9781266686764
Author: Colander
Publisher: MCG
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Chapter 20.1, Problem 6Q
To determine

Describe the optimal strategy for the first player.

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Consider a beauty-contest game in which n players simultaneously pick a number between zero and 100 inclusive; the person whose number is closer to half of the average number wins a prize. What is the unique Nash equilibrium of this game? What number will a level-3 thinker pick?
Suppose that you and a friend play a matching pennies game in which each of you uncovers a penny. If both pennies show heads or both show tails, you keep both. If one shows heads and the other shows tails, your friend keeps them. Show the pay- off matrix. What, if any, is the pure-strategy Nash equilibrium to this game? Is there a mixed-strategy Nash equilibrium? If so, what is it?
Which player (if any) has a dominate strategy? What is the Nash Equilibrium of this game? Does the game satisfy the definition of prisoner dilemma?
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