Econ 521 - Week 6:
1. Find all Nash Equilibria in the following games
(a) Prisoner's Dilemma
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2
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C
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S
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1
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C
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1,1
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3,0
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S
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0,3
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2,2
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(b) Battle of the Sexes
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2
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B
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S
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1
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B
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2,1
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0,0
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S
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0,0
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1,2
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(c) Matching Pennies
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2
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H
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T
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1
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H
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1,-1
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-1,1
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T
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-1,1
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1,-1
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2. A coordination game - Two people can perform a task if, and only if, they both exert effort. They are both better off if they both exert effort and perform the task than if neither exerts effort (and nothing is accomplished); the worst outcome for each person is that she exerts effort and the other person does not (in which case again nothing is accomplished). Specifically, the player's preferences are represented by the expected value of the payoff functions in the following figure, Where c is a positive number less than 1 that can be
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2
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N
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E
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1
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N
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0,0
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0,-c
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E
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-c,0
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1-c,1-c
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interpreted as the cost of exerting effort. Find all mixed strategy Nash equilibria of this game. How do the equilibria change as c increases? Explain the reasons for the changes.
3. Find all mixed strategy Nash equilibria of the following game
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2
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X
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Y
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Z
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1
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A
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2,2
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0,3
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1,3
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B
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3,2
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1,1
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0,2
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