6. Consider the following game: a. Identify all Nash Equilibria (Pure Strategy and Mixed) of this...
6. Consider the following game:
a. Identify all Nash Equilibria (Pure Strategy and Mixed) of this simultaneous game.
b. Draw the two extensive form games that arise from each firm moving first. What are the Subgame Perfect Equilibria of these games?
c. Identify a trigger strategy for each player that sustains (B,B) as an equilibrium. For what interest (discount) rates will this outcome be sustainable?
Homework Answers
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6. Consider the following game:
a. Identify all Nash Equilibria (Pure Strategy and Mixed) of
this...
Consider the following game: a) Identify all Nash Equilibria (Pure Strategy and Mixed) of this simultaneous...
Consider the following game:
a) Identify all Nash
Equilibria (Pure Strategy and Mixed) of this simultaneous game.
b) Identify a trigger strategy for
each player that sustains (B,B) as an equilibrium in an infinitely
repeated game. For what interest(discount) rates will this outcome
be sustainable?
Firm 2 А B A -5,-5 195,-50 Firm 1 -50,215 45,75
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash...
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultan...
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultaneous-move games. Player B LeftRight 6,5 2,1 Up 0,1 Player A 6,11 Down Player B LeftRight 1,4 0,16 2,13 4,3 Up Player A Down
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultaneous-move games. Player B LeftRight 6,5 2,1 Up 0,1 Player A 6,11 Down Player B LeftRight 1,4 0,16 2,13 4,3 Up Player A Down
Some Game Theory Problems 3. Find all of the pure strategy Nash Equilibria of the following simultaneous move game....
Some Game Theory Problems 3. Find all of the pure strategy Nash Equilibria of the following simultaneous move game. After solving it as a simultaneous move game, write it as a sequential move game with column moving first. Drow the game tree and solve for the Subgame Perfect Nash Equilibrium. Column 9,4 1,10 15,7 15,5 14,8 3,10 12,18 20,12 Row C 7,8 6,8 20,10 3,3 15,9 15,0 14,2 9,1 20,18 2,9 10,14 19,20
a.) Find all pure-strategy Nash equilibria. b.) *Find all mixed-strategy Nash equilibria. c.) Explain why, in...
a.) Find all pure-strategy Nash equilibria.
b.) *Find all mixed-strategy Nash equilibria.
c.) Explain why, in any mixed-strategy equilibrium, each player
must be indifferent between the pure strategies that she randomizes
over.
Consider the following game: - 2 LR 2
Determine ALL of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following 3 games: Player...
Determine ALL of the Nash equilibria
(pure-strategy and mixed-strategy equilibria) of
the following 3 games:
Player 1 H T Player 2 HT (1, -1) (-1,1) | (-1,1) (1, -1) | Н Player 1 H D Player 2 D (2, 2) (3,1) | (3,1) |(2,2) | Player 2 A (2, 2) (0,0) Player 1 A B B (0,0) | (3,4)
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game...
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game? What is the Subgame Perfect Equilibrium? 2. Represent this game as a Normal form game and find all pure strategy Nash Eq. Is there a mixed Nash eq. in this game? If yes, show one. If not, argue why not 3. Now assume that P2 cannot observe P1's action before he makes his move. As such, he...
For each tree, find all pure strategy Nash equilibria (NE), and all pure strategy subgame-perfect Nash...
For each tree, find all pure strategy Nash equilibria (NE), and all pure strategy subgame-perfect Nash equilibria (SPNE). In every tree, payoffs are in alphabetical order. You can gain up to 10 points per tree (5 points for NE, 5 points for SPNE)
In the extensive form representation of the game between Player 1 and Player 2, Player 1...
In the extensive form representation of the game between Player 1 and Player 2, Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has______________ pure strategy Nash equilibria and__________ pure strategy Subgame Perfect Nash Equilibria (SPNE). The maximum payoff Player 2 gets in a SPNE is___________ . (Please, enter only numerical answers like: 1, 2,...
#2. Find all pure and mixed strategy Nash equilibria (if any) in the following game. U...
#2. Find all pure and mixed strategy Nash equilibria (if any) in the following game. U 1,1 0,0 0, -1 S 0,0 1,1 0, -1 D.0.0 0,-1
Consider the following game:
a) Identify all Nash
Equilibria (Pure Strategy and Mixed) of this simultaneous game.
b) Identify a trigger strategy for
each player that sustains (B,B) as an equilibrium in an infinitely
repeated game. For what interest(discount) rates will this outcome
be sustainable?
Firm 2 А B A -5,-5 195,-50 Firm 1 -50,215 45,75
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultaneous-move games. Player B LeftRight 6,5 2,1 Up 0,1 Player A 6,11 Down Player B LeftRight 1,4 0,16 2,13 4,3 Up Player A Down
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultaneous-move games. Player B LeftRight 6,5 2,1 Up 0,1 Player A 6,11 Down Player B LeftRight 1,4 0,16 2,13 4,3 Up Player A Down
Some Game Theory Problems 3. Find all of the pure strategy Nash Equilibria of the following simultaneous move game. After solving it as a simultaneous move game, write it as a sequential move game with column moving first. Drow the game tree and solve for the Subgame Perfect Nash Equilibrium. Column 9,4 1,10 15,7 15,5 14,8 3,10 12,18 20,12 Row C 7,8 6,8 20,10 3,3 15,9 15,0 14,2 9,1 20,18 2,9 10,14 19,20
a.) Find all pure-strategy Nash equilibria.
b.) *Find all mixed-strategy Nash equilibria.
c.) Explain why, in any mixed-strategy equilibrium, each player
must be indifferent between the pure strategies that she randomizes
over.
Consider the following game: - 2 LR 2
Determine ALL of the Nash equilibria
(pure-strategy and mixed-strategy equilibria) of
the following 3 games:
Player 1 H T Player 2 HT (1, -1) (-1,1) | (-1,1) (1, -1) | Н Player 1 H D Player 2 D (2, 2) (3,1) | (3,1) |(2,2) | Player 2 A (2, 2) (0,0) Player 1 A B B (0,0) | (3,4)
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game? What is the Subgame Perfect Equilibrium? 2. Represent this game as a Normal form game and find all pure strategy Nash Eq. Is there a mixed Nash eq. in this game? If yes, show one. If not, argue why not 3. Now assume that P2 cannot observe P1's action before he makes his move. As such, he...
For each tree, find all pure strategy Nash equilibria (NE), and all pure strategy subgame-perfect Nash equilibria (SPNE). In every tree, payoffs are in alphabetical order. You can gain up to 10 points per tree (5 points for NE, 5 points for SPNE)
#2. Find all pure and mixed strategy Nash equilibria (if any) in the following game. U 1,1 0,0 0, -1 S 0,0 1,1 0, -1 D.0.0 0,-1
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