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2. Consider the extensive form game shown in the figure below. The top payoff at a terminal node ...
Question 1 o, 0 0 21 2 0 0 Consider the extensive form game portrayed above....
Question 1 o, 0 0 21 2 0 0 Consider the extensive form game portrayed above. The top number at a terminal node is player 1's payoff, the middle number is player 2's payoff and the bottom number is player 3's payof. a. Derive the strategy set for each player. (Note: If you do not want to list all of the strategies, you can provide a general description of a player's strategy, give an example, and state how many strategies...
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...
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...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2,...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2, 2) (2, 2) (0, 6) (6, 0 (0,0 (6, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy Bayesian Nash equilibrium (equilibria) b) Find pure strategy subgame perfect equilibrium (or equilibria) of this game. c) Find pure strategy perfect Bayesian equilibrium (or equilibria) of this game.
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice....
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice. If player 1 chooses H, then player 2 must choose A or B. Player 1 does not get to observe this choice by player 2, and must then choose X or Y. If A and X are played, the payoff for player 1 is 1 and for player 2 it's 5. If A and Y are played, the payoff for player 1 is 6...
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,...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)
1. Consider the following extensive form game with perfect information: 2 In 0 (a) (Level A)...
1. Consider the following extensive form game with perfect information: 2 In 0 (a) (Level A) Write down the normal form associated with this extensive formm game (b) (Level A) First suppose = 0. Find a subgame perfect equilibrium for this game. (c) (Level B) Again suppose α-0. Find a pure strategy Nash equilibrium of this extensive form game that is not subgame perfect. (d) (Level B) Now suppose α = 3. Find all pure strategy subgame perfect equi- libria....
4. (General Extensive Form Game ID Suppose the following general extensive-form game. Player 1 Player 2...
4. (General Extensive Form Game ID Suppose the following general extensive-form game. Player 1 Player 2 (0, 4) (4,0 (4, 0) (0, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy (Bayesian Nash equilibrium (equilibria) b) Does a pure strategy perfect Bayesian equilibrium exist? If so, show it (or them). If not, prove it.
Q.1 Consider the following extensive-form game: Playxo Playr 2 o Player? 8, 6 8,5 7, 6...
Q.1 Consider the following extensive-form game: Playxo Playr 2 o Player? 8, 6 8,5 7, 6 9, 7 Q.1.a Depict the corresponding normal form of the game. Q.1.b Identify the Nash equilibria. Q.1.c Identify the subgame-perfect Nash equilibrium by using backward induction.
Question 1 o, 0 0 21 2 0 0 Consider the extensive form game portrayed above. The top number at a terminal node is player 1's payoff, the middle number is player 2's payoff and the bottom number is player 3's payof. a. Derive the strategy set for each player. (Note: If you do not want to list all of the strategies, you can provide a general description of a player's strategy, give an example, and state how many strategies...
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...
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...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2, 2) (2, 2) (0, 6) (6, 0 (0,0 (6, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy Bayesian Nash equilibrium (equilibria) b) Find pure strategy subgame perfect equilibrium (or equilibria) of this game. c) Find pure strategy perfect Bayesian equilibrium (or equilibria) of this game.
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)
1. Consider the following extensive form game with perfect information: 2 In 0 (a) (Level A) Write down the normal form associated with this extensive formm game (b) (Level A) First suppose = 0. Find a subgame perfect equilibrium for this game. (c) (Level B) Again suppose α-0. Find a pure strategy Nash equilibrium of this extensive form game that is not subgame perfect. (d) (Level B) Now suppose α = 3. Find all pure strategy subgame perfect equi- libria....
4. (General Extensive Form Game ID Suppose the following general extensive-form game. Player 1 Player 2 (0, 4) (4,0 (4, 0) (0, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy (Bayesian Nash equilibrium (equilibria) b) Does a pure strategy perfect Bayesian equilibrium exist? If so, show it (or them). If not, prove it.
Q.1 Consider the following extensive-form game: Playxo Playr 2 o Player? 8, 6 8,5 7, 6 9, 7 Q.1.a Depict the corresponding normal form of the game. Q.1.b Identify the Nash equilibria. Q.1.c Identify the subgame-perfect Nash equilibrium by using backward induction.
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