Microeconomic Theory Assignment
1. What is a "strategy" in game theory? Provide its definition briefly. 2 . What i s a " Nash equilibrium"?
3. Find the unique Nash equilibrium in the following game (Prisoner's Dilemma)
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Player 2
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Deny
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Confess
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Player 1
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Deny
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-1,-1
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-20,0
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Confess
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0,- 20
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-5, -5
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4 . Find two pure-strategy Nash equilibrium in the following game (Battle of Sexes)
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Wife
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Soccer
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Opera
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Husband
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Soccer
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2, 1
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0, 0
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Opera
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0, 0
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1, 2
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5 . Show that there does not exist a pure-strategy Nash equilibrium in the following game (Matching pennies)
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Player 2
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Head
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Tail
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Player 1
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Head
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1 ,- 1
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- 1 , 1
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Tail
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- 1 , 1
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1 ,- 1
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6 . I n the game given i n 5, show that it is a mixed-strategy equilibrium that both players play each action with probability 1/2.
7. What is a "subgame perfect Nash equilibrium"? Provide its definition briefly.
8. Find a subgame perfect Nash equilibrium of the following extensive-form game.
9 . Find a s u bga m e perfect Nash equilibrium of the following extensive-form game.
