What is the difference between subgame perfect Nash equilibrium and Nash equilibrium of an extensive form game?
What is the difference between subgame perfect Nash equilibrium and Nash equilibrium of an extensive form game?
Homework Answers
A subgame perfect nash equilibrium is a nash equilibrium profile in every subgame of an extensive game whereas a nash equilibrium in an extensive game is derived by first converting it into a normal form game and then scouting for optimal strategies of either player which also includes off the equilibrium path strategies which have non credible threat.
The latter gets eliminated in subgame perfect equilibrium which is scouted using backward induction.
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What is the difference between subgame perfect Nash equilibrium and Nash equilibrium of an extensive form game?
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....
Froblem #5: Convert extensive-form to strategic-form, find Nash equilibria and subgame. perfect Nash equilibria (12...
Froblem #5: Convert extensive-form to strategic-form, find Nash equilibria and subgame. perfect Nash equilibria (12pts) Consider the following extensive-form game: Veto Y Don't Veto In this game, Players 1 and 2 are deciding on a course of action, which may be X, Y, or Z Player 2 is the one who actually makes the choice, but first Player may choose to veto Y, which is the option Player 1 prefers the least. a) List all the strategies available to Player...
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...
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.
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-...
find all subgame perfect nash equilibria (SPE )for the following game 1. Find all subgame perfect...
find all subgame perfect nash equilibria (SPE )for the following
game
1. Find all subgame perfect Nash equilibria (SPE) in the following game: 5, 6 9, 8 Y2, 6 6, 7 ?3.9 7,4 5, 5
Game Theory Economics If its stage game has exactly one Nash equilibrium, how many subgame perfect...
Game Theory Economics If its stage game has exactly one Nash equilibrium, how many subgame perfect equilibria does a two-period, repeated game have? Explain. Would this answer change if there were T periods, where T is any finite integer?
4. If its stage game has exactly one Nash equilibrium, how many subgame perfect equilibria does...
4. If its stage game has exactly one Nash equilibrium, how many subgame perfect equilibria does a two-period, repeated game have? Explain. Would your answer change if there were Tperiods, where Tis any finite integer?
A) Consider the extensive form game of complete and imperfect information above. The number of pure...
A) Consider the extensive form game of complete and imperfect
information above. The number of pure strategy Nash Equilibrium in
the game is? (Please, type only numerical values, for example: 0,
1, 2, 3,....)
B) Consider the extensive form game of complete and imperfect
information above. The following strategy profiles are Subgame
Perfect Nash Equilibrium (Select all that apply)
a) (WY, AD)
b) (WY, AC)
c) (ZX, AD)
d) (ZY, BC)
e) (ZY, BD)
...
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....
Froblem #5: Convert extensive-form to strategic-form, find Nash equilibria and subgame. perfect Nash equilibria (12pts) Consider the following extensive-form game: Veto Y Don't Veto In this game, Players 1 and 2 are deciding on a course of action, which may be X, Y, or Z Player 2 is the one who actually makes the choice, but first Player may choose to veto Y, which is the option Player 1 prefers the least. a) List all the strategies available to Player...
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...
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 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-...
find all subgame perfect nash equilibria (SPE )for the following
game
1. Find all subgame perfect Nash equilibria (SPE) in the following game: 5, 6 9, 8 Y2, 6 6, 7 ?3.9 7,4 5, 5
4. If its stage game has exactly one Nash equilibrium, how many subgame perfect equilibria does a two-period, repeated game have? Explain. Would your answer change if there were Tperiods, where Tis any finite integer?
A) Consider the extensive form game of complete and imperfect
information above. The number of pure strategy Nash Equilibrium in
the game is? (Please, type only numerical values, for example: 0,
1, 2, 3,....)
B) Consider the extensive form game of complete and imperfect
information above. The following strategy profiles are Subgame
Perfect Nash Equilibrium (Select all that apply)
a) (WY, AD)
b) (WY, AC)
c) (ZX, AD)
d) (ZY, BC)
e) (ZY, BD)
...
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