Game Theory Nash Equilibrium Mixed strategies for 2*3 Matrix
a) Eliminate strictly dominated strategies.
b) If the game does not have a pure strategy Nash equilibrium,
find the mixed strategy Nash equilibrium for the smaller game
(after eliminating dominated strategies).
Player 2 | ||||
Player 1 | a | b | c | |
A | 4,3 | 3,2 | 2,4 | |
B | 1,3 | 5,3 | 3,3 | |
Homework Answers
Request Answer!
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? What are the Nash equilibria of these games? (a) Player 2 Left 0,2 1,3 2,4 Top Middle Bottom Center 4,3 2,4 1,5 Right 3, 4 2, 3 4,6 Player 1 (b) Player 2 Left 2,4 3,3 4,6 Top Middle Bottom Center 6,5 4,3 5,4 Player 1 Right 5,3 4, 2 2,5
Problem 1. Consider the following extensive form game. 2 > 2,3 4,1 3,2 1.2 (a) By...
Problem 1. Consider the following extensive form game. 2 > 2,3 4,1 3,2 1.2 (a) By converting the game into normal form game (by finding the corre- sponding bimatrix game), find all Nash equilibrium in pure strategies. (b) Does player 2 have a strictly dominated strategy?
Please answer 3 Questions, thank you. 4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7)...
Please answer 3 Questions, thank you.
4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7) PLAYER 1 (2,4) (0,6) (2,0) (1,3) (2,4) (0,3) a) Does this game have any pure-strategy Nash equilibrium? If so, identify it (or them) and explain why this is an equilibrium. b) Find a mixed-strategy Nash equilibrium to this game and explain your calculations. Note: a mixed strategy for player i may be expressed by o; = (P1, P2, 1- P1 - p2). c) Is...
(2,5). Find the Walrasian equilibrium. 4. 120] Answer the following. (a) 14 Explain the difference between...
(2,5). Find the Walrasian equilibrium. 4. 120] Answer the following. (a) 14 Explain the difference between a strategy that is a best response versus a strategy that is strictly dominant. (b) (6) Consider the following game: player 2 D E F C A 3,7 7,3 1,2 4,3 player 1 B 8,9 8,5 2,8 5,2 C 0,10 7,01,9 2,2 Find the strictly dominant strategies solution and the iterated elimination of strictly dominated strategies solution, if any. (c) [10] Consider the following...
7. Consider the following two player game, with the players being 1 and 2. As usual...
7. Consider the following two player game, with the players being 1 and 2. As usual 1 chooses a row and 2 a column. ABC a 1,4 2,1 3,2 4,1 b 2,3 3,4 4,3 1,2 с 3,1 4,2 1,4 2,3 d 4,2 1,3 4,3 3,2 (a) Which strategies satisfy iterated elimination of strictly dominated strategies? How many levels of knowledge of rationality do you have to assume to obtain your result? (b) If you were allowed to follow the same...
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...
Problem 2: Consider the following normal form game: | A | B | C D L...
Problem 2: Consider the following normal form game: | A | B | C D L 2 ,3 -1,3 0,0 4,3 M -1,0 3,0 / 0,10 2,0 R 1,1 | 2,1 3,1 3,1 Part a: What are the pure strategies that are strictly dominated in the above game? Part 6: What are the rationalizable strategies for each player? What are all the rationalizable strategy profiles? Part c: Find all of the Nash equilibria of the game above.
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and...
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and iterated elimination of strictly dominated strategies solution. That is, does one solution concept imply the other? (b) (5) Consider the following game: player 2 E F G H A-10,6 10.0 3,8 4.-5 player 1 B 9,8 14,8 4.10 2,5 C-10,3 5,9 8.10 5,7 D 0,0 3,10 8,12 0,8 Does any player have a strictly dominant strategies? Find the strictly dominant strategies solution and the...
3. For the game represented below 1) Modify the game matrix by eliminating dominated strategies 2)...
3. For the game represented below 1) Modify the game matrix by eliminating dominated strategies 2) Find a Nash Equilibrium in pure strategies. 3) Find NE in mixed strategies Y 3; 4 2; 2 3,5 D 2;3 1; 5 Z 5; 2 2;1 3:3 0:4 3; 0
4. Consider the following game matrix: LCR T 3 ,1 0,0 4,1 M10, 02, 24, 3...
4. Consider the following game matrix: LCR T 3 ,1 0,0 4,1 M10, 02, 24, 3 B 7,6 | 1,2 3,1 (a) Find all the strictly dominated (pure) strategies for each player. (b) Find all the weakly dominated (pure) strategies of each player. (c) Does the game has a strict dominant strategy equilibrium?
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? What are the Nash equilibria of these games? (a) Player 2 Left 0,2 1,3 2,4 Top Middle Bottom Center 4,3 2,4 1,5 Right 3, 4 2, 3 4,6 Player 1 (b) Player 2 Left 2,4 3,3 4,6 Top Middle Bottom Center 6,5 4,3 5,4 Player 1 Right 5,3 4, 2 2,5
Problem 1. Consider the following extensive form game. 2 > 2,3 4,1 3,2 1.2 (a) By converting the game into normal form game (by finding the corre- sponding bimatrix game), find all Nash equilibrium in pure strategies. (b) Does player 2 have a strictly dominated strategy?
Please answer 3 Questions, thank you.
4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7) PLAYER 1 (2,4) (0,6) (2,0) (1,3) (2,4) (0,3) a) Does this game have any pure-strategy Nash equilibrium? If so, identify it (or them) and explain why this is an equilibrium. b) Find a mixed-strategy Nash equilibrium to this game and explain your calculations. Note: a mixed strategy for player i may be expressed by o; = (P1, P2, 1- P1 - p2). c) Is...
(2,5). Find the Walrasian equilibrium. 4. 120] Answer the following. (a) 14 Explain the difference between a strategy that is a best response versus a strategy that is strictly dominant. (b) (6) Consider the following game: player 2 D E F C A 3,7 7,3 1,2 4,3 player 1 B 8,9 8,5 2,8 5,2 C 0,10 7,01,9 2,2 Find the strictly dominant strategies solution and the iterated elimination of strictly dominated strategies solution, if any. (c) [10] Consider the following...
7. Consider the following two player game, with the players being 1 and 2. As usual 1 chooses a row and 2 a column. ABC a 1,4 2,1 3,2 4,1 b 2,3 3,4 4,3 1,2 с 3,1 4,2 1,4 2,3 d 4,2 1,3 4,3 3,2 (a) Which strategies satisfy iterated elimination of strictly dominated strategies? How many levels of knowledge of rationality do you have to assume to obtain your result? (b) If you were allowed to follow the same...
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...
Problem 2: Consider the following normal form game: | A | B | C D L 2 ,3 -1,3 0,0 4,3 M -1,0 3,0 / 0,10 2,0 R 1,1 | 2,1 3,1 3,1 Part a: What are the pure strategies that are strictly dominated in the above game? Part 6: What are the rationalizable strategies for each player? What are all the rationalizable strategy profiles? Part c: Find all of the Nash equilibria of the game above.
4. [20] Answer the following. (a) (5) State the relationship between strictly dominant strategies solution and iterated elimination of strictly dominated strategies solution. That is, does one solution concept imply the other? (b) (5) Consider the following game: player 2 E F G H A-10,6 10.0 3,8 4.-5 player 1 B 9,8 14,8 4.10 2,5 C-10,3 5,9 8.10 5,7 D 0,0 3,10 8,12 0,8 Does any player have a strictly dominant strategies? Find the strictly dominant strategies solution and the...
3. For the game represented below 1) Modify the game matrix by eliminating dominated strategies 2) Find a Nash Equilibrium in pure strategies. 3) Find NE in mixed strategies Y 3; 4 2; 2 3,5 D 2;3 1; 5 Z 5; 2 2;1 3:3 0:4 3; 0
4. Consider the following game matrix: LCR T 3 ,1 0,0 4,1 M10, 02, 24, 3 B 7,6 | 1,2 3,1 (a) Find all the strictly dominated (pure) strategies for each player. (b) Find all the weakly dominated (pure) strategies of each player. (c) Does the game has a strict dominant strategy equilibrium?
Most questions answered within 3 hours.
-
Reynold company is considering an investment of $130,000 in
new equipment. The new equipment is expected...
asked 14 minutes ago -
If a company’s stock price (P0) goes up, and nothing else
changes, Ke (the required rate...
asked 1 minute ago -
As a manager in today society, how can I use Harry Truman's
leadership skills and attributes...
asked 3 minutes ago -
The decomposition of SO2Cl2 is first order
and has a rate constant of + 2.90 x...
asked 3 minutes ago -
Why is protecting equipment an important element of this
concept, and how are some of the...
asked 13 minutes ago -
An asset used in a four-year project falls in the five-year
MACRS class (MACRS Table) for...
asked 14 minutes ago -
Break-even time. Hampton Corporation’s research
and development department is presenting a proposal for new product
research....
asked 18 minutes ago -
At Lake Itasca in Minnesota, the Mississippi river is only 25.0
feet wide. If you are...
asked 19 minutes ago -
A 2.0 μF parallel-plate air-filled capacitor is connected
across a 10 V battery.
(a) Determine the...
asked 29 minutes ago -
Write in Python This program:
1. Correct the compute_cells_state function which receives as
parameter an array...
asked 19 minutes ago -
1. What is the difference in the output layer between a neural
network used for classification,...
asked 27 minutes ago -
ECO
2013 &
asked 34 minutes ago