Homework Answers
A game is a strategic interaction between two players. The payoff of the game is written in tabular form is called the strategic form. The payoff wrote in this manner has two numbers in each cell of the table separated by a comma. The first number denotes the payoff of row player while the second number denotes payoff of column player. Each row denotes strategy of row player. In this case, row player is player 1, with strategies A and B. The column player is player 2 with strategies C, D, and E. The when 1 plays A and 2 plays E, the payoff implied by this move is given in upper right corner cell. The payoff of 1 is 2 and payoff of 2 is 1.
Therefore, the correct option is: (b)
Player lI C D E A 0,0 0,2 2,1 В 1,2 1,1 0,0 Player B Consider...
Player lI C D E A 0,0 0,2 2,1 В 1,2 1,1 0,0 Player B Consider the strategic form game above and select all that apply. Strategy A is not dominant for Player 1. Strategy B is weakly dominant for player I. Strategy E is dominated by strategies C and D for player 2. Strategy E is never a best response.
QUESTTON 4 Player Il E D A 3,34,21,4 B 2,0 3,0-1,1 с 1,1 2,1 0,2 Player...
QUESTTON 4 Player Il E D A 3,34,21,4 B 2,0 3,0-1,1 с 1,1 2,1 0,2 Player Consider the game above. Select all that apply. a Strategy B weakly dominates C. Strategy D weakly dominates E. c. The game does not have a dominant strategy solution. d. F is a dominant strategy. e. (A,D) is the dominant strategy solution.
Player II D E F A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5...
Player II D E F A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider the game above. Suppose Player 1 conjectures that Player 2 plays D with probability 1/4, E with probability 1/8, and F with probability 5/8. Player 1's best response to her conjecture about Player 2's strategy is to play a. A b. B OC.C . Another mixed strategy.
Player II A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider...
Player II A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider the strategic form game above. The number of strategies player 1 has is and player 2 moves at information sets (Please write numerical values like 0,1, 74, etc.)
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...
Player II A x5 0,4 4,4 В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider...
Player II A x5 0,4 4,4 В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider the game above. Suppose Player 1 conjectures that Player 2 plays D with probability 1/4, E with probability 1/8, and F with probability 5/8. The value of X that makes Player 1 randomize evenly between strategies A and C (i.e., play p=(12, 0, 1/2)) is [x]. Please, do not use fractional forms; if your answer is -1/2 use -0.5 instead
Player Il D EF A 5,3 3,5 8,5 В 1,2 0,2 9,3 С 6,3 2,4 8,9...
Player Il D EF A 5,3 3,5 8,5 В 1,2 0,2 9,3 С 6,3 2,4 8,9 Player The game above has a Nash Equilibrium in which Player 1 plays strategy and Player 2 plays strategy E with probability at least (Please, do not use fractions, if your answer is 2/5 use 0.4)
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...
d e f a 2,6 0,4 4,4 b 3,3 0,0 1,5 c 1,1 3,5 2,3...
d e f a 2,6 0,4 4,4 b 3,3 0,0 1,5 c 1,1 3,5 2,3 Consider the strategic form game above. The number of strategies player 1 has is_______ and player 2 moves at___________ information sets (Please write numerical values like 0,1, 74, etc.).
Player lI C D E A 0,0 0,2 2,1 В 1,2 1,1 0,0 Player B Consider the strategic form game above and select all that apply. Strategy A is not dominant for Player 1. Strategy B is weakly dominant for player I. Strategy E is dominated by strategies C and D for player 2. Strategy E is never a best response.
QUESTTON 4 Player Il E D A 3,34,21,4 B 2,0 3,0-1,1 с 1,1 2,1 0,2 Player Consider the game above. Select all that apply. a Strategy B weakly dominates C. Strategy D weakly dominates E. c. The game does not have a dominant strategy solution. d. F is a dominant strategy. e. (A,D) is the dominant strategy solution.
Player II D E F A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider the game above. Suppose Player 1 conjectures that Player 2 plays D with probability 1/4, E with probability 1/8, and F with probability 5/8. Player 1's best response to her conjecture about Player 2's strategy is to play a. A b. B OC.C . Another mixed strategy.
Player II A 2,6 0A 4A В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider the strategic form game above. The number of strategies player 1 has is and player 2 moves at information sets (Please write numerical values like 0,1, 74, etc.)
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...
Player II A x5 0,4 4,4 В 3,3 0,0 1,5 С 1,1 3,5 2,3 Player Consider the game above. Suppose Player 1 conjectures that Player 2 plays D with probability 1/4, E with probability 1/8, and F with probability 5/8. The value of X that makes Player 1 randomize evenly between strategies A and C (i.e., play p=(12, 0, 1/2)) is [x]. Please, do not use fractional forms; if your answer is -1/2 use -0.5 instead
Player Il D EF A 5,3 3,5 8,5 В 1,2 0,2 9,3 С 6,3 2,4 8,9 Player The game above has a Nash Equilibrium in which Player 1 plays strategy and Player 2 plays strategy E with probability at least (Please, do not use fractions, if your answer is 2/5 use 0.4)
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...
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