Homework Answers
Answer) The sub game perfect nash equilibrium describes the set of strategy whereby neither of the player has an incentive to deviate from a given strategy. To attain sub game Nash equilibrium, the technique of backward induction is used at a given node.
The two Subgame nash equilibrium are:
- (L,l,x)
- (M,a)
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
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....
1. Consider the following extensive form game with perfect information 1 Out 2 2 In 3...
1. Consider the following extensive form game with perfect information 1 Out 2 2 In 3 3 a) (Level A) Write down the normal form associated with this extensive form 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 ash equilibrium of this extensive form game that is not subgame perfect (d) (Level B) Now suppose a-3. Find all pure strategy subgame perfect equi-...
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...
The extensive form of a 2pemon game as follones R. (a) What are the pure strategy...
The extensive form of a 2pemon game as follones R. (a) What are the pure strategy sets for players I and II. (b) Derive the normal (strategie) form of the game? (e) Use backward induction to find the sub-game perfect Nash Equi- librium of the game. (d) Find the other Nash Equilibrium and explain why it is not sub game perfect.
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...
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.
3. The extensive form of a 2-person game is as follows: 1/ 2 020210 0 0-25-210...
3. The extensive form of a 2-person game is as follows: 1/ 2 020210 0 0-25-210 (a) What are the pure strategy sets for players I and II. (b) Derive the normal (strategic) form of the game? (c) Find the Nash Equilibrium(a) of the game (d) Is there any sub-game non-perfect equilibrium? Explain.
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
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....
1. Consider the following extensive form game with perfect information 1 Out 2 2 In 3 3 a) (Level A) Write down the normal form associated with this extensive form 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 ash equilibrium of this extensive form game that is not subgame perfect (d) (Level B) Now suppose a-3. Find all pure strategy subgame perfect equi-...
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...
The extensive form of a 2pemon game as follones R. (a) What are the pure strategy sets for players I and II. (b) Derive the normal (strategie) form of the game? (e) Use backward induction to find the sub-game perfect Nash Equi- librium of the game. (d) Find the other Nash Equilibrium and explain why it is not sub game perfect.
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...
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.
3. The extensive form of a 2-person game is as follows: 1/ 2 020210 0 0-25-210 (a) What are the pure strategy sets for players I and II. (b) Derive the normal (strategic) form of the game? (c) Find the Nash Equilibrium(a) of the game (d) Is there any sub-game non-perfect equilibrium? Explain.
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