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 information regarding input and output. This is not needed to solve the problem.
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A hundred players are participating in this game (N = 100). Each
player has to choose...
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...
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...
4. (a) (10%) A player has three information sets in the game tree. He has four...
4. (a) (10%) A player has three information sets in the game tree. He has four choices in his first information set, four in his second and three in his third. How many strategies does he have in the strategic form? Circle one: (i) 11, (ii) 28 (iii) 48 (iv) 18. (b) (10%) Is it true that the following game is a Prisoners' Dilemma? Explain which features of a Prisoners' Dilemma hold and which do not. (Remember each player must...
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?
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...
Dominance: Ten players simultaneously and noncooperatively each pick a real number in [0,1]. Let their choices...
Dominance: Ten players simultaneously and noncooperatively each pick a real number in [0,1]. Let their choices be X1, X2, ....X10. Let X be the average of all the x's. The game proceeds as follows. Everyone picks their value x. Then the average X is calculated. Whichever of the players guesses closest to 2/3 the value of X wins $1 and all other players get nothing. If there is a tie, then they flip coins for a single winner. Can this...
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...
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...
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...
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...
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...
4. (a) (10%) A player has three information sets in the game tree. He has four choices in his first information set, four in his second and three in his third. How many strategies does he have in the strategic form? Circle one: (i) 11, (ii) 28 (iii) 48 (iv) 18. (b) (10%) Is it true that the following game is a Prisoners' Dilemma? Explain which features of a Prisoners' Dilemma hold and which do not. (Remember each player must...
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?
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...
Dominance: Ten players simultaneously and noncooperatively each pick a real number in [0,1]. Let their choices be X1, X2, ....X10. Let X be the average of all the x's. The game proceeds as follows. Everyone picks their value x. Then the average X is calculated. Whichever of the players guesses closest to 2/3 the value of X wins $1 and all other players get nothing. If there is a tie, then they flip coins for a single winner. Can 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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