6. (a) For the following extensive-form game: 1. Identify the pure and mixed strategy Nash Equilibria. i. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria of the game different from the set of equilibria identified in parf (a)? Explain (a couple of sentences should suffice). (3,1) Player 1 A D (-2,-2) B Player 2 b₁ b₂ ay 3,0 0,1 az 2,1 2,1 с (2,5) D (b) Consider the simultaneous-move game below with two players, 1 and 2. Each player has two pure strategies. If a player plays both strategies with strictly positive probability, we call it a strictly mixed strategy for that player. Show that there is no Nash equilibrium in which both 1 and 2 play a strictly mixed strategy. (0,7)
6. (a) For the following extensive-form game: 1. Identify the pure and mixed strategy Nash Equilibria. i. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria of the game different from the set of equilibria identified in parf (a)? Explain (a couple of sentences should suffice). (3,1) Player 1 A D (-2,-2) B Player 2 b₁ b₂ ay 3,0 0,1 az 2,1 2,1 с (2,5) D (b) Consider the simultaneous-move game below with two players, 1 and 2. Each player has two pure strategies. If a player plays both strategies with strictly positive probability, we call it a strictly mixed strategy for that player. Show that there is no Nash equilibrium in which both 1 and 2 play a strictly mixed strategy. (0,7)
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.9P
Related questions
Question
![6. (a) For the following extensive-form game:
1. Identify the pure and mixed strategy Nash Equilibria.
ii. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria
of the game different from the set of equilibria identified in parf (a)?
Explain (a couple of sentences should suffice).
с
(3,1)
Player 1 a
a2
A
D
(-2,-2)
B
Player 2
bi
b₂
3,0
0,1
2,1 2,1
C
(2,5)
D
(b) Consider the simultaneous-move game below with two players, 1 and 2.
Each player has two pure strategies. If a player plays both strategies with
strictly positive probability, we call it a strictly mixed strategy for that
player. Show that there is no Nash equilibrium in which both 1 and 2 play
a strictly mixed strategy.
(0,7)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12cc7796-a235-4914-a517-f128b03fefe7%2F71048c52-49e9-4994-8320-e7e13f59d125%2Fwh87drm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. (a) For the following extensive-form game:
1. Identify the pure and mixed strategy Nash Equilibria.
ii. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria
of the game different from the set of equilibria identified in parf (a)?
Explain (a couple of sentences should suffice).
с
(3,1)
Player 1 a
a2
A
D
(-2,-2)
B
Player 2
bi
b₂
3,0
0,1
2,1 2,1
C
(2,5)
D
(b) Consider the simultaneous-move game below with two players, 1 and 2.
Each player has two pure strategies. If a player plays both strategies with
strictly positive probability, we call it a strictly mixed strategy for that
player. Show that there is no Nash equilibrium in which both 1 and 2 play
a strictly mixed strategy.
(0,7)
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