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Imagine a two-player game that proceeds as follows. A pot of money is created with $6 in it initially. Player 1 moves first, then player 2, then player 1 again, and finally player 2 again. At each player's turn to move, he has two possible actions: grab G or share S. If he grabs he gets 2/3 of the current pot of money, the other player gets 1/3 of the pot, and the game ends. If he shares then the size of the current pot is multiplied by 3/2 and the next player gets to move. At the last stage at which player 2 moves, if he chooses S then the pot is still multiplied by 3/2, player 2 gets 1/3 of the pot, and player 1 gets 2/3 of the pot. Which of the following is an SPE? 1) (G, G) 2)(GS, GS) 3) (GG, GG)

Imagine a two-player game that proceeds as follows. A pot of money is created with $6 in it initially. Player 1 moves first, then player 2, then player 1 again, and finally player 2 again. At each player's turn to move, he has two possible actions: grab G or share S. If he grabs he gets 2/3 of the current pot of money, the other player gets 1/3 of the pot, and the game ends. If he shares then the size of the current pot is multiplied by 3/2 and the next player gets to move. At the last stage at which player 2 moves, if he chooses S then the pot is still multiplied by 3/2, player 2 gets 1/3 of the pot, and player 1 gets 2/3 of the pot. Which of the following is an SPE? 1) (G, G) 2)(GS, GS) 3) (GG, GG)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 36EQ
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Imagine a two-player game that proceeds as follows. A pot of money is created with $6 in it initially. Player 1 moves first, then player 2, then player 1 again, and finally player 2 again. At each player's turn to move, he has two possible actions: grab G or share S. If he grabs he gets 2/3 of the current pot of money, the other player gets 1/3 of the pot, and the game ends. If he shares then the size of the current pot is multiplied by 3/2 and the next player gets to move. At the last stage at which player 2 moves, if he chooses S then the pot is still multiplied by 3/2, player 2 gets 1/3 of the pot, and player 1 gets 2/3 of the pot. Which of the following is an SPE? 1) (G, G) 2) (GS, GS) 3) (GG, GG) 4) (SG, SG)
Transcribed Image Text:Imagine a two-player game that proceeds as follows. A pot of money is created with $6 in it initially. Player 1 moves first, then player 2, then player 1 again, and finally player 2 again. At each player's turn to move, he has two possible actions: grab G or share S. If he grabs he gets 2/3 of the current pot of money, the other player gets 1/3 of the pot, and the game ends. If he shares then the size of the current pot is multiplied by 3/2 and the next player gets to move. At the last stage at which player 2 moves, if he chooses S then the pot is still multiplied by 3/2, player 2 gets 1/3 of the pot, and player 1 gets 2/3 of the pot. Which of the following is an SPE? 1) (G, G) 2) (GS, GS) 3) (GG, GG) 4) (SG, SG)
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