6. Solve the following game (see next page) in extensive form. What are the actions chosen by player 1 (a or a*, then c or c* if applicable) and the action chosen by player 2 (b or b*) in equilibrium? What are the resulting profit for each player?
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6. Solve the following game (see next page) in extensive form. What are the actions chosen by pla...
5. (General Extensive Form Game IID Suppose the following general extensive-form game. Note that denotes the...
5. (General Extensive Form Game IID Suppose the following general extensive-form game. Note that denotes the belief that the player 2's decision node after Player 1 chooses Ais reached. Player 1 (2, 2) Player 2 a, 0) (3, 1 (a) Find the conditions on parameter values (a and b) such that (B,X) witlh 0 is the perfect Bayesian equilibrium, if any (b) Find the conditions on parameter values (a and b) such that (C,Y) is the strategy profile of the...
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.
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.
Question 2 Consider the following extensive form game. R 2 a А/ B 2,3 / 1...
Question 2 Consider the following extensive form game. R 2 a А/ B 2,3 / 1 \ь 3, x 3,0 1, Each value of x defines a different game. 1. Solve this game by backward induction for x = 0 and for x = 2. For each of those values of x, what are the payoffs that player 2 can get in the solution? 2. Write this game in Normal form (The table can have an entry of the form...
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...
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...
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...
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....
Consider the following extensive form game. What is the subgame perfect equilibrium path in this game?...
Consider the following extensive form game.
What is the subgame perfect equilibrium path in this game?
1 L R M 2 2 1 а) r b а/ь 0 X 2 0 0 2 0 -1 у X у 1 1 2 -1 1 10 0 0 1
5. (General Extensive Form Game IID Suppose the following general extensive-form game. Note that denotes the belief that the player 2's decision node after Player 1 chooses Ais reached. Player 1 (2, 2) Player 2 a, 0) (3, 1 (a) Find the conditions on parameter values (a and b) such that (B,X) witlh 0 is the perfect Bayesian equilibrium, if any (b) Find the conditions on parameter values (a and b) such that (C,Y) is the strategy profile of the...
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.
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.
Question 2 Consider the following extensive form game. R 2 a А/ B 2,3 / 1 \ь 3, x 3,0 1, Each value of x defines a different game. 1. Solve this game by backward induction for x = 0 and for x = 2. For each of those values of x, what are the payoffs that player 2 can get in the solution? 2. Write this game in Normal form (The table can have an entry of the form...
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...
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...
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....
Consider the following extensive form game.
What is the subgame perfect equilibrium path in this game?
1 L R M 2 2 1 а) r b а/ь 0 X 2 0 0 2 0 -1 у X у 1 1 2 -1 1 10 0 0 1
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