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 |
|
- Is there pure strategy Nash Equilibrium in this game? If yes, find it/them out. If no, explain.
- What is the mixed strategy Nash Equilibrium in this game? Find it/them out and show your steps.
Homework Answers
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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We know that Kyle loves playing Lego with Zack more than just
playing Lego by himself....
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