Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R 1 player I's payoff 000 2 O player 2's payoff O player 3's payoff M 3 b 0 1 1 010 1 0 1 2 221 2 0 000 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.
Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R 1 player I's payoff 000 2 O player 2's payoff O player 3's payoff M 3 b 0 1 1 010 1 0 1 2 221 2 0 000 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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![Exercise 6.8. Consider the following extensive-form game with cardinal payoffs:
1
Σ
R
1 player I's payoff
O player 2's payoff
O player 3's payoff
000
2
a
b
3
a
0
1
1
010
0
222
2
2
1
P
000
(a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect?
(b) [This is a more challenging question] Prove that there is no mixed-strategy Nash
equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50b68c8b-7bbf-421c-bb9e-cf8a245ca404%2Ffcdd8029-7ef6-4013-b21a-86bc0efa5932%2Fqgjggi8_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 6.8. Consider the following extensive-form game with cardinal payoffs:
1
Σ
R
1 player I's payoff
O player 2's payoff
O player 3's payoff
000
2
a
b
3
a
0
1
1
010
0
222
2
2
1
P
000
(a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect?
(b) [This is a more challenging question] Prove that there is no mixed-strategy Nash
equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.
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