Consider a two-player game in which the players take turns, with player 1 moving first. When it is a player's turn, she must announce a number between 1 and 3. The announced number is added to the previously announced numbers. The player who announces the number such that the sum of all announced numbers is 6 wins (receives 1) and the other loses (receives 0). Please indicate whether or not each of the following sequences of announcements is a Nash equilibrium of the game. Hint: Think about how one verifies whether or not a pair of strategies is a Nash equilibrium. P1 says 3, then P2 says 2, then P1 says 1 P1 says 1, then P2 says 3, then P1 says 2 P1 says 2, then P2 says 3, then P1 says 1 P1 says 3, then P2 says 1, then P1 says 2
Consider a two-player game in which the players take turns, with player 1 moving first. When it is a player's turn, she must announce a number between 1 and 3. The announced number is added to the previously announced numbers. The player who announces the number such that the sum of all announced numbers is 6 wins (receives 1) and the other loses (receives 0). Please indicate whether or not each of the following sequences of announcements is a Nash equilibrium of the game. Hint: Think about how one verifies whether or not a pair of strategies is a Nash equilibrium. P1 says 3, then P2 says 2, then P1 says 1 P1 says 1, then P2 says 3, then P1 says 2 P1 says 2, then P2 says 3, then P1 says 1 P1 says 3, then P2 says 1, then P1 says 2
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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![Consider a two-player game in which the players take turns, with player 1 moving first. When it is a player's turn,
she must announce a number between 1 and 3. The announced number is added to the previously announced
numbers. The player who announces the number such that the sum of all announced numbers is 6 wins (receives
1) and the other loses (receives 0). Please indicate whether or not each of the following sequences of
announcements is a Nash equilibrium of the game.
Hint: Think about how one verifies whether or not a pair of strategies is a Nash equilibrium.
P1 says 3, then P2 says 2, then P1 says 1
P1 says 1, then P2 says 3, then P1 says 2
P1 says 2, then P2 says 3, then P1 says 1
P1 says 3, then P2 says 1, then P1 says 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fec5f0b-3332-4e83-8b1c-3dcc90cc5025%2Fc2c129ca-e179-4f2a-aa86-2b832caa97cb%2F6xfsb7j_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a two-player game in which the players take turns, with player 1 moving first. When it is a player's turn,
she must announce a number between 1 and 3. The announced number is added to the previously announced
numbers. The player who announces the number such that the sum of all announced numbers is 6 wins (receives
1) and the other loses (receives 0). Please indicate whether or not each of the following sequences of
announcements is a Nash equilibrium of the game.
Hint: Think about how one verifies whether or not a pair of strategies is a Nash equilibrium.
P1 says 3, then P2 says 2, then P1 says 1
P1 says 1, then P2 says 3, then P1 says 2
P1 says 2, then P2 says 3, then P1 says 1
P1 says 3, then P2 says 1, then P1 says 2
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