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We know that Kyle loves playing Lego with Zack more than just playing Lego by himself....

We know that Kyle loves playing Lego with Zack more than just playing Lego by himself. Kyle enjoys playing Puzzles himself rather than playing with Zack. Zack always enjoys playing with his big brother than playing by himself.

Zack

Kyle

Lego

Puzzles

Lego

5, 5

4, 2

Puzzles

6, 3

2, 5
  1. Is there pure strategy Nash Equilibrium in this game? If yes, find it/them out. If no, explain.
  2. What is the mixed strategy Nash Equilibrium in this game? Find it/them out and show your steps.
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Answer #1

Lego Lego is a pure-strategy Nash Equilibrium (since in this case the probability of playing a particular strategy is 1 for each player)

A B
1 5 2
2 3 5


A: 5x + 3(1 - x)=2x+3
B: 2x + 5(1 - x)=5-3x
2x+3 = 5-3x
Therefore, x = 2/5
Player 1 should play 1: 2/5, 2: 3/5

A B
1 5 4
2 6 2


1: 5x + 4(1 - x)=x+4
2: 6x + 2(1 - x)=4x+2
x+4 =4x+2
Therefore, x = 2/3
Player 2 should play A: 2/3, B: 1/3

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