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1 Consider the following normal-form game. P2 L CR P M (a) Does Pl (player 1)...
(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)...
Q2 Contribution Game Consider the following game. There are four players. Each player i (wherei 1,2,3,4)...
Q2 Contribution Game Consider the following game. There are four players. Each player i (wherei 1,2,3,4) si multaneously and independently selects her contribution s E [0, 10]. Each player gets a benefit related to all of the players choices of s,'s, but incurs a cost related to her own contribution s In particular, the payoff to each player i is given by: ul (s1 , s2, s3, s.) = si + s2 + s3 + 84-0.5s (a) Find best response...
Can someone tell me how to solve this question? Q1. Consider the following game L CR...
Can someone tell me how to solve this question?
Q1. Consider the following game L CR T2,21,14,2 M 3,41,22,3 B 1,3 0,2 3,0 a. Which strategies survive iterated deletion of strictly dominated strategies? (3 marks) b. What are the pure-strategy Nash equilibria? Explain why these are Nash equilibria. (3 marks) c. Why are the strictly dominated strategies not part of a Nash equilibrium? (2 marks)
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.
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.
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...
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...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies S = {U,D), S2 L, R, S3 - {A, B). The payoffs are summarized in the following payoff matrices: Table 3: Payoff Matrices P3 P3 plays A P2 P3 plays B P2 U|3,3,8 1,2,-2 D 0,9,6 -4,13 , -2 ,1 U 11,-1,2 9,5,12 DI 0,1,4 3,-1 , 3 P1 where in an cell the payoff x , y , z corresponds to P1, P2...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods. Consider the...
Question 1 a) First consider the following game, where each player plays either C (Confess) or D ...
Question 1 a) First consider the following game, where each player plays either C (Confess) or D (Deny) and the numbers in brackets are the respective payoffs to player 1 and player 2. Player 2 Player 1 (0-12) (-12,0) In relation to the above game outline the concepts of - Dominated strategies - Best responses - Nash equilibrium/equilibria - A prisoner's dilemma b) Define what is meant by subgame perfection and how the concept of credibility can be used to...
(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)...
Q2 Contribution Game Consider the following game. There are four players. Each player i (wherei 1,2,3,4) si multaneously and independently selects her contribution s E [0, 10]. Each player gets a benefit related to all of the players choices of s,'s, but incurs a cost related to her own contribution s In particular, the payoff to each player i is given by: ul (s1 , s2, s3, s.) = si + s2 + s3 + 84-0.5s (a) Find best response...
Can someone tell me how to solve this question?
Q1. Consider the following game L CR T2,21,14,2 M 3,41,22,3 B 1,3 0,2 3,0 a. Which strategies survive iterated deletion of strictly dominated strategies? (3 marks) b. What are the pure-strategy Nash equilibria? Explain why these are Nash equilibria. (3 marks) c. Why are the strictly dominated strategies not part of a Nash equilibrium? (2 marks)
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.
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.
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...
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...
3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies S = {U,D), S2 L, R, S3 - {A, B). The payoffs are summarized in the following payoff matrices: Table 3: Payoff Matrices P3 P3 plays A P2 P3 plays B P2 U|3,3,8 1,2,-2 D 0,9,6 -4,13 , -2 ,1 U 11,-1,2 9,5,12 DI 0,1,4 3,-1 , 3 P1 where in an cell the payoff x , y , z corresponds to P1, P2...
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods. Consider the...
Question 1 a) First consider the following game, where each player plays either C (Confess) or D (Deny) and the numbers in brackets are the respective payoffs to player 1 and player 2. Player 2 Player 1 (0-12) (-12,0) In relation to the above game outline the concepts of - Dominated strategies - Best responses - Nash equilibrium/equilibria - A prisoner's dilemma b) Define what is meant by subgame perfection and how the concept of credibility can be used to...
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