Homework Answers
| Player1/ Player 2 | C | D | |||||||
| C | 300|300 | (-)100|(-)100 | |||||||
| D | (-)100|(-)100 | x|x | |||||||
| For player 1 | |||||||||
| If player 2 choose C player 1 will go for C because of higher pay off of 300 vs -100 | |||||||||
| IF player 2 choose D player 1 should not be going for C because there should not be a dominant strategy for player 1, | |||||||||
| so the pay offs should be structured in that way, He will select for D when pay off is greater than -100 | |||||||||
| For player 2 | |||||||||
| If player 1 choose C player 2 will go for C because of higher pay off of 300 vs -100 | |||||||||
| IF player 1 choose D player 2 shoul not be going for C because there should not be a dominant strategy for player 2, | |||||||||
| so the pay offs should be structured in that way, He will select for D when pay off is greater than -100 | |||||||||
| Nash Equilibrium | |||||||||
| Basis the strategies they will select I have underlined the payoffs | |||||||||
| In order to have a single Nash equilibrium x <300 | |||||||||
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Player 2 C D C 300,300 -100,-100 Player 1 D -100,-100 1,0 Figure 1: A Flexible...
3. Consider the following game in normal form. Player 1 is the "row" player with strate-...
3. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, z. The game is presented in the following matrix: W Z X y a 3,3 2,1 0,2 2,1 b 1,1 1,2 1,0 1,4 0,0 1,0 3,2 1,1 d 0,0 0,5 0,2 3,1 с Find all the Nash equilibria in the game in pure strategies.
1. Consider the following game in normal form. Player 1 is the "row" player with strate-...
1. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, 2. The game is presented in the following matrix: a b c d w 3,3 1,1 0,0 0,0 x 2,1 1,2 1,0 0,5 y 0,2 1,0 3, 2 0,2 z 2,1 1,4 1,1 3,1 (a) Find the set of rationalizable strategies. (b) Find the set of Nash...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
1. Consider the following two-player game in strategic form: T4,5 3,0 0,2 M 5,2 2, 1,0 B0,02,84,2...
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Could you help me with this question ASAP
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1. Consider the following two-player game in strategic form: T4,5 3,0 0,2 M 5,2 2, 1,0 B0,02,84,2 (a) What strategies are rationalizable? (b) What strategies survive the iterative elimination of strictly dominant strategies? (c) What strategies are ruled out by the assumption of rationality alone (i.e, without the assumption of common knowledge)? (d) Find all pure-strategy nash equilibria.
1. Consider the following two-player game in strategic form: T4,5...
DLM R A 2,3 -1,0 1,1 B -1,3 3,0 2,1 C 0,0 0,10 3,1 D 4,3...
DLM R A 2,3 -1,0 1,1 B -1,3 3,0 2,1 C 0,0 0,10 3,1 D 4,3 2,0 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.
Consider the following game: Player2 U Player 1 M 100.99 0.0 99 100 0.0 1.1 0.0...
Consider the following game: Player2 U Player 1 M 100.99 0.0 99 100 0.0 1.1 0.0 99. 10000 100.99 a. Does player 1 have a strictly dominant strategy? If the answer is yes, write the dominant strategy in the specified area and if the answer is no just write no b. Does player 2 have a strictly dominant strategyIf the answer is yes, write the dominant strategy in the specified area and if the answer is no just write no...
player 2 H T player 1 H 1,-1 -1,1 T -1,1 1,-1 Consider a game of...
player 2 H T player 1 H 1,-1 -1,1 T -1,1 1,-1 Consider a game of matching pennies as described above. If the pennies match player 2 pays player 1 $1 (both get head or tail). If the pennies are not matched player 1 pays player 2 $1 ( head , tail or tail , head). H represents heads and T represents Tails 1. (2 points) What is the set of strategies for each player? 2. (5 points) Is there...
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,...
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,0 3,2 0,3 This game will demonstrate several methods for ruling out possible mixed- strategy equilibria (a) What are the pure strategy equilibria? (b) Show that there does not exist an equilibrium in which Player 1 (the row player) assigns strictly positive probability to A, to B, and to C. (c) Show that there does not exist an equilibrium in...
2. (15) Consider the following game: Player 2 C D 6,8 3,9 4,10 7,7 Player 1...
2. (15) Consider the following game: Player 2 C D 6,8 3,9 4,10 7,7 Player 1 A B (a) Find all pure strategy Nash equilibria of this game. (5) (b) Find the mixed strategy Nash equilibrium of this game. Be sure to show your work. (10)
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?
3. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, z. The game is presented in the following matrix: W Z X y a 3,3 2,1 0,2 2,1 b 1,1 1,2 1,0 1,4 0,0 1,0 3,2 1,1 d 0,0 0,5 0,2 3,1 с Find all the Nash equilibria in the game in pure strategies.
1. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, 2. The game is presented in the following matrix: a b c d w 3,3 1,1 0,0 0,0 x 2,1 1,2 1,0 0,5 y 0,2 1,0 3, 2 0,2 z 2,1 1,4 1,1 3,1 (a) Find the set of rationalizable strategies. (b) Find the set of Nash...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
Hello tutor,
Could you help me with this question ASAP
Thank you.
1. Consider the following two-player game in strategic form: T4,5 3,0 0,2 M 5,2 2, 1,0 B0,02,84,2 (a) What strategies are rationalizable? (b) What strategies survive the iterative elimination of strictly dominant strategies? (c) What strategies are ruled out by the assumption of rationality alone (i.e, without the assumption of common knowledge)? (d) Find all pure-strategy nash equilibria.
1. Consider the following two-player game in strategic form: T4,5...
DLM R A 2,3 -1,0 1,1 B -1,3 3,0 2,1 C 0,0 0,10 3,1 D 4,3 2,0 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.
Consider the following game: Player2 U Player 1 M 100.99 0.0 99 100 0.0 1.1 0.0 99. 10000 100.99 a. Does player 1 have a strictly dominant strategy? If the answer is yes, write the dominant strategy in the specified area and if the answer is no just write no b. Does player 2 have a strictly dominant strategyIf the answer is yes, write the dominant strategy in the specified area and if the answer is no just write no...
player 2 H T player 1 H 1,-1 -1,1 T -1,1 1,-1 Consider a game of matching pennies as described above. If the pennies match player 2 pays player 1 $1 (both get head or tail). If the pennies are not matched player 1 pays player 2 $1 ( head , tail or tail , head). H represents heads and T represents Tails 1. (2 points) What is the set of strategies for each player? 2. (5 points) Is there...
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,0 3,2 0,3 This game will demonstrate several methods for ruling out possible mixed- strategy equilibria (a) What are the pure strategy equilibria? (b) Show that there does not exist an equilibrium in which Player 1 (the row player) assigns strictly positive probability to A, to B, and to C. (c) Show that there does not exist an equilibrium in...
2. (15) Consider the following game: Player 2 C D 6,8 3,9 4,10 7,7 Player 1 A B (a) Find all pure strategy Nash equilibria of this game. (5) (b) Find the mixed strategy Nash equilibrium of this game. Be sure to show your work. (10)
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?
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