1. Consider the following sequential game:Left(3,5)MaryGo(6,4)UpRightJohnStop(5.7)John(a) Draw the game tree of the game.JohnGoDown(4,1)LeftMaryStop(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 oneof two actions, continue or stop, with Eve choosing first. Each time a player sayscontinue, $10 will be removed from her pile, and $20 will be added to the otherplayer's pile. The game automatically stops when the total amount in their pilesreaches $60.(Eve as player 1 and Noa as player 2)(b) By backward induction, find a Nash equilibrium and the corresponding payoffs.

Nash equilibrium is a concept in game theory that describes a stable state of a strategic…

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.

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.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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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