A group of 7 players play the following game. Each writes down a positive integer that...
A group of 7 players play the following game. Each writes down
a positive integer that is less than 1000. The player who writes down the
smallest number is awarded a prize equal to the number of dollars equal to
the number that she wrote down. If there is a tie for smallest number, the
prize is divided equally among those who wrote the smallest number. Find
the strategy or strategies that survive iterated deletion of strictly dominated
strategies. Explain your answer.
Homework Answers
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A group of 7 players play the following game. Each writes
down
a positive integer that...
Some notes: A hundred players are participating in this game (N 100). Each player has to...
Some notes:
A hundred players are participating in this game (N 100). Each player has to choose an integer between 1 and 100 in order to guess "5/6 of the average of the responses given by all players". Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins (a) Q4 Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies (IEDS) (if any)...
Iterated Iterated elimination of dominated strategies: Eliminate all strictly (weakly) dominated strategies for all players in...
Iterated
Iterated elimination of dominated strategies:
Eliminate all strictly (weakly) dominated strategies for all
players in the original game.
Eliminate all strictly (weakly) dominated strategies for all
players in the modified game where players cannot choose any
strategy that was eliminated at Step 1.
3 Eliminate all strictly (weakly) dominated strategies for all
players in the modified game where players cannot choose any
strategy that was eliminated at Steps 1 and 2.
4 ...
and so on until there are...
(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)...
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...
3. On the first day of class we played the beauty contest in which n players...
3. On the first day of class we played the beauty contest in which n players submitted a number in the interval [0, 10 and the player closest to won (with ties broke by randomization). Here š denotes the average strategy played 3 (a) What strategies survive iterative deletion of strictly dominated strategies? (b) What are the Nash equiliburia of the game?
Game Theory Iterated Elimination: In the following normal-form game, which strategy profiles survive iterated elimination of...
Game Theory
Iterated Elimination: In the following normal-form game, which strategy profiles survive iterated elimination of strictly dominated strategies? 4.5 Player 2 L C R 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 D 8,10 4,6 6,7
Ldn and Cathy play a game of matching fingers. On a predeter ned signal, both players smultaneous...
ldn and Cathy play a game of matching fingers. On a predeter ned signal, both players smultaneously extend 2 or 3 fingers from a closed fist if the sm of the number of fingers extended s even, then Robin receives an amount in dollars equal to that sum from Cathy. If the sum of the numbers of fingers extended is odd, then Cathy receives an amount in dollars equal to that sum from Robin (a) Construct the payoff matrix for...
Q3 Guess 5/6 of the Average Game A hundred players are participating in this game (N-100)....
Q3 Guess 5/6 of the Average Game A hundred players are participating in this game (N-100). Each player has to choose an integer between 1 and 100 in order to guess "5/6 of the average of the responses given by all players'" Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins (a) Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies...
A hundred players are participating in this game (N = 100). Each player has to choose...
A hundred players are participating in this game (N = 100). Each player has to choose an integer between 1 and 100 in order to guess “5/6 of the average of the responses given by all players”. Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins. (a) Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies (IEDS) (if any). No additional...
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)
Some notes:
A hundred players are participating in this game (N 100). Each player has to choose an integer between 1 and 100 in order to guess "5/6 of the average of the responses given by all players". Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins (a) Q4 Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies (IEDS) (if any)...
Iterated
Iterated elimination of dominated strategies:
Eliminate all strictly (weakly) dominated strategies for all
players in the original game.
Eliminate all strictly (weakly) dominated strategies for all
players in the modified game where players cannot choose any
strategy that was eliminated at Step 1.
3 Eliminate all strictly (weakly) dominated strategies for all
players in the modified game where players cannot choose any
strategy that was eliminated at Steps 1 and 2.
4 ...
and so on until there are...
(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)...
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...
3. On the first day of class we played the beauty contest in which n players submitted a number in the interval [0, 10 and the player closest to won (with ties broke by randomization). Here š denotes the average strategy played 3 (a) What strategies survive iterative deletion of strictly dominated strategies? (b) What are the Nash equiliburia of the game?
Game Theory
Iterated Elimination: In the following normal-form game, which strategy profiles survive iterated elimination of strictly dominated strategies? 4.5 Player 2 L C R 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 D 8,10 4,6 6,7
ldn and Cathy play a game of matching fingers. On a predeter ned signal, both players smultaneously extend 2 or 3 fingers from a closed fist if the sm of the number of fingers extended s even, then Robin receives an amount in dollars equal to that sum from Cathy. If the sum of the numbers of fingers extended is odd, then Cathy receives an amount in dollars equal to that sum from Robin (a) Construct the payoff matrix for...
Q3 Guess 5/6 of the Average Game A hundred players are participating in this game (N-100). Each player has to choose an integer between 1 and 100 in order to guess "5/6 of the average of the responses given by all players'" Each player who guesses the integer closest to the 5/6 of the average of all the responses, wins (a) Find all weakly dominated strategies (if any). (b) Find all strategies that survive the Iterative Elimination of Dominated Strategies...
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)
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