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Player 1 and player 2 are playing a simultaneous-move one-shot game, where player 1 can move "up" or "down" and player 2 can move "left" or "right." The payoffs for the game are shown in the payoff matrix. The first number of each cell represents player 1's payoff, and the second number is player 2's. Use the matrix to answer the questions below. Player 1 2nd attempt Part 1 Part 2 Which of the following outcomes is a pure strategy Nash equilibrium of this game? Up Down p= (1-P) = q= Left -16, -18 -20,7 Choose one or more: A. There is no pure strategy Nash equilibrium in this game. B. Player 1 plays up; player 2 plays left. C. Player 1 plays up; player 2 plays right. Part 3 Player 2 □ D. Player 1 plays down; player 2 plays left. D E. Player 1 plays down; player 2 plays right. Right -17, -20 -14, 10 Suppose player 1 assigns probability p to playing up and (1-p) to playing down. What do p and (1-p) have to be such that player 2 is indifferent between playing left and right? Round all answers to two decimal places. (1-q) = Suppose player 2 assigns probability q to playing left and (1-q) to playing right. What do q and (1-q) have to be such that player 1 is indifferent between playing up and down? Round all answers to two decimal places.

Player 1 and player 2 are playing a simultaneous-move one-shot game, where player 1 can move "up" or "down" and player 2 can move "left" or "right." The payoffs for the game are shown in the payoff matrix. The first number of each cell represents player 1's payoff, and the second number is player 2's. Use the matrix to answer the questions below. Player 1 2nd attempt Part 1 Part 2 Which of the following outcomes is a pure strategy Nash equilibrium of this game? Up Down p= (1-P) = q= Left -16, -18 -20,7 Choose one or more: A. There is no pure strategy Nash equilibrium in this game. B. Player 1 plays up; player 2 plays left. C. Player 1 plays up; player 2 plays right. Part 3 Player 2 □ D. Player 1 plays down; player 2 plays left. D E. Player 1 plays down; player 2 plays right. Right -17, -20 -14, 10 Suppose player 1 assigns probability p to playing up and (1-p) to playing down. What do p and (1-p) have to be such that player 2 is indifferent between playing left and right? Round all answers to two decimal places. (1-q) = Suppose player 2 assigns probability q to playing left and (1-q) to playing right. What do q and (1-q) have to be such that player 1 is indifferent between playing up and down? Round all answers to two decimal places.

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.8P
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Player 1 and player 2 are playing a simultaneous-move one-shot game, where player 1 can move "up" or "down" and player 2 can move "left" or "right" The payoffs for the game are shown in the payoff matrix. The first number of each cell represents player 1's payoff, and the second number is player 2's. Use the matrix to answer the questions below. Player 1 2nd attempt Part 1 Part 2 Which of the following outcomes is a pure strategy Nash equilibrium of this game? P = (1-P) = Up Down Part 3 9= Left -16, -18 -20,7 Choose one or more: A. There is no pure strategy Nash equilibrium in this game. OB. Player 1 plays up; player 2 plays left. OC. Player 1 plays up; player 2 plays right. □ D. Player 1 plays down; player 2 plays left. O E. Player 1 plays down; player 2 plays right. Player 2 Suppose player 1 assigns probability p to playing up and (1 - p) to playing down. What do p and (1-p) have to be such that player 2 is indifferent between playing left and right? Round all answers to two decimal places. Right -17, -20 -14, 10 (1-q) = Suppose player 2 assigns probability to playing left and (1-q) to playing right. What do q and (1 - g) have to be such that player 1 is indifferent between playing up and down? Round all answers to two decimal places.
Transcribed Image Text:Player 1 and player 2 are playing a simultaneous-move one-shot game, where player 1 can move "up" or "down" and player 2 can move "left" or "right" The payoffs for the game are shown in the payoff matrix. The first number of each cell represents player 1's payoff, and the second number is player 2's. Use the matrix to answer the questions below. Player 1 2nd attempt Part 1 Part 2 Which of the following outcomes is a pure strategy Nash equilibrium of this game? P = (1-P) = Up Down Part 3 9= Left -16, -18 -20,7 Choose one or more: A. There is no pure strategy Nash equilibrium in this game. OB. Player 1 plays up; player 2 plays left. OC. Player 1 plays up; player 2 plays right. □ D. Player 1 plays down; player 2 plays left. O E. Player 1 plays down; player 2 plays right. Player 2 Suppose player 1 assigns probability p to playing up and (1 - p) to playing down. What do p and (1-p) have to be such that player 2 is indifferent between playing left and right? Round all answers to two decimal places. Right -17, -20 -14, 10 (1-q) = Suppose player 2 assigns probability to playing left and (1-q) to playing right. What do q and (1 - g) have to be such that player 1 is indifferent between playing up and down? Round all answers to two decimal places.
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