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Exercise 4. In the following matriz, the mized strategy that assigns probability 1/2 to M and...
4. [20] Answer the following. (a) [4] Explain the difference between a strategy that is a...
4. [20] Answer the following. (a) [4] 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 G A 3,7 7,3 1,2 4,3 player 1 B 89 8,5 2,8 5,2 C | 0.10 | 7.0 | 1.9 | 2.2 Find the strictly dominant strategies solution and the iterated elimination of strictly dominated strategies solution, if any. (c) [10] Consider the following...
Exercise 4 - Pure strategies that are only strictly dominated by a mixed strategy Consider the...
Exercise 4 - Pure strategies that are only strictly dominated by a mixed strategy Consider the following normal form game Player 2 Left Right Player 1 4,1 Down 13 12 b) Is there some strictly dominated strategy for player 1 when mixed strategies are allowed? [Hint: 0,2 4,1 Middle0,0 a) c) d) Is there some strictly dominated strategy for player 1 involving only the use of pure strategies? you may assign probabilities to two of her strategies, similarly as we...
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...
(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)...
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...
1. (Dominated Strategies) Find strictly dominant strategy, strictly dominated strategy, weakly dominant strategy, and weakly dominated...
1. (Dominated Strategies) Find strictly dominant strategy, strictly dominated strategy, weakly dominant strategy, and weakly dominated strategy of the following two games("None" may be an answer). Do not forget to discuss about mixed strategies too. (a) (Keio and Waseda) Player 2 K E O Wa 6,1 2,3 0,2 Player 1 Se 3,00,0,0 Da 2,0 1,2 01 b) (NHK BS) Player 2 BS N 41 0,2 Player 1 H 0,0 4,0 Problems 6 and 7 are in the next pages
(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...
2. Iterative Deletion of (weakly) Dominated Strategies Consider the following two-player game 2 I c I...
2. Iterative Deletion of (weakly) Dominated Strategies Consider the following two-player game 2 I c I T 1,1 0,1 3,1 1 M 1,0 2,2 1,3 D 1,3 3,1 2,2 (a) Are there any strictly dominated strategies? Are there any weakly dominated strategies? If so, explain what dominates what and how. (b) After deleting any strictly or weakly dominated strategies, are there any strictly or weakly dominated strategies in the reduced' game? If so, explain what dominates what and how. What...
Exercise 6 (Difficult),. Consider the following modification of the prisoner's dilemma game. A-1,...
Exercise 6 (Difficult),. Consider the following modification of the prisoner's dilemma game. A-1,-1-9,0-6,-2 B | 0,-9 |-6-61-5-10 C1-2,-6 |-10,-51-4,-4 You should recognise the payoff's from (A, L), (A, R). (B, L). (B, R) as those in the prisoner's dilemma game studied in class. We added two strategies, one for each player. Also note that strategies A and L are still (when compared to the original prisoner's dilemma game) strictly dominated . What is the set of Nash equilibria of this...
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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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...
4. [20] Answer the following. (a) [4] 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 G A 3,7 7,3 1,2 4,3 player 1 B 89 8,5 2,8 5,2 C | 0.10 | 7.0 | 1.9 | 2.2 Find the strictly dominant strategies solution and the iterated elimination of strictly dominated strategies solution, if any. (c) [10] Consider the following...
Exercise 4 - Pure strategies that are only strictly dominated by a mixed strategy Consider the following normal form game Player 2 Left Right Player 1 4,1 Down 13 12 b) Is there some strictly dominated strategy for player 1 when mixed strategies are allowed? [Hint: 0,2 4,1 Middle0,0 a) c) d) Is there some strictly dominated strategy for player 1 involving only the use of pure strategies? you may assign probabilities to two of her strategies, similarly as we...
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...
(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)...
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...
1. (Dominated Strategies) Find strictly dominant strategy, strictly dominated strategy, weakly dominant strategy, and weakly dominated strategy of the following two games("None" may be an answer). Do not forget to discuss about mixed strategies too. (a) (Keio and Waseda) Player 2 K E O Wa 6,1 2,3 0,2 Player 1 Se 3,00,0,0 Da 2,0 1,2 01 b) (NHK BS) Player 2 BS N 41 0,2 Player 1 H 0,0 4,0 Problems 6 and 7 are in the next pages
(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...
2. Iterative Deletion of (weakly) Dominated Strategies Consider the following two-player game 2 I c I T 1,1 0,1 3,1 1 M 1,0 2,2 1,3 D 1,3 3,1 2,2 (a) Are there any strictly dominated strategies? Are there any weakly dominated strategies? If so, explain what dominates what and how. (b) After deleting any strictly or weakly dominated strategies, are there any strictly or weakly dominated strategies in the reduced' game? If so, explain what dominates what and how. What...
Exercise 6 (Difficult),. Consider the following modification of the prisoner's dilemma game. A-1,-1-9,0-6,-2 B | 0,-9 |-6-61-5-10 C1-2,-6 |-10,-51-4,-4 You should recognise the payoff's from (A, L), (A, R). (B, L). (B, R) as those in the prisoner's dilemma game studied in class. We added two strategies, one for each player. Also note that strategies A and L are still (when compared to the original prisoner's dilemma game) strictly dominated . What is the set of Nash equilibria of this...
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...
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