Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 1 000 2 R M 3 1 Player's payoff 0 player 2 payoff O player 3's payoff о 1 1 9 010 221 E 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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Exercise 6.8. Consider the following extensive-form game with cardinal payoffs:
1
R
O player pay
000
2
1
M
3
b
010
O player 3's payoff
1
2
221
2
000
0
0
(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.
Transcribed Image Text:Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (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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