1. Consider the following sequential game: Left (3,5) Mary Go (6,4) Up Right John Stop (5.7) John John Go Down (4.1) Left Mary Stop (2.5) Right (6,-1) (John as player 1 and Mary as player 2) By backward induction, find a Nash equilibrium and the corresponding payoffs.

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Chapter1: Making Economics Decisions
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1. Consider the following sequential game:
Left
(3,5)
Mary
Go
(6,4)
Up
Right
John
Stop
(5.7)
John
(a) Draw the game tree of the game.
John
Go
Down
(4,1)
Left
Mary
Stop
(2,5)
Right
(6,-1)
(John as player 1 and Mary as player 2)
By backward induction, find a Nash equilibrium and the corresponding payoffs.
2. Eve and Noa start with $10 in each of their piles. They take turns choosing one
of two actions, continue or stop, with Eve choosing first. Each time a player says
continue, $10 will be removed from her pile, and $20 will be added to the other
player's pile. The game automatically stops when the total amount in their piles
reaches $60.
(Eve as player 1 and Noa as player 2)
(b) By backward induction, find a Nash equilibrium and the corresponding payoffs.
Transcribed Image Text:1. Consider the following sequential game: Left (3,5) Mary Go (6,4) Up Right John Stop (5.7) John (a) Draw the game tree of the game. John Go Down (4,1) Left Mary Stop (2,5) Right (6,-1) (John as player 1 and Mary as player 2) By backward induction, find a Nash equilibrium and the corresponding payoffs. 2. Eve and Noa start with $10 in each of their piles. They take turns choosing one of two actions, continue or stop, with Eve choosing first. Each time a player says continue, $10 will be removed from her pile, and $20 will be added to the other player's pile. The game automatically stops when the total amount in their piles reaches $60. (Eve as player 1 and Noa as player 2) (b) By backward induction, find a Nash equilibrium and the corresponding payoffs.
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