Consider the following perfect information sequential move game between Player 1 andPlayer 2, where x is an integer. Player 1 is the leader and moves first, while Player 2 is thefollower and moves second, after observing Player 1's move.0i.Illustrate the rollback process and find the equilibrium path for every possible valueof x. What are the payoffs to each player at the quilibrium outcome?li.Describe the full set of available strategies available to each Player. Choose one ofthe strategies for each Player and describe what it means.Describe the rollback equilibrium by providing and using the complete strategiesemployed by each Player for every possible value of x.25toyBO24NX

Given information 2 players player 1 and player 2 Given game is sequential game with perfect…

Consider the following perfect information sequential move game between Player 1 and Player 2, where x is an integer. Player 1 is the leader and moves first, while Player 2 is the follower and moves second, after observing Player 1's move. C N D E B 2 F

Consider the following perfect information sequential move game between Player 1 and Player 2, where x is an integer. Player 1 is the leader and moves first, while Player 2 is the follower and moves second, after observing Player 1's move. C N D E B 2 F

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

Consider the following perfect information sequential move game between Player 1 and
Player 2, where x is an integer. Player 1 is the leader and moves first, while Player 2 is the
follower and moves second, after observing Player 1's move.
0
i.
Illustrate the rollback process and find the equilibrium path for every possible value
of x. What are the payoffs to each player at the quilibrium outcome?
li.
Describe the full set of available strategies available to each Player. Choose one of
the strategies for each Player and describe what it means.
Describe the rollback equilibrium by providing and using the complete strategies
employed by each Player for every possible value of x.
25
toy
BO
2
4
NX

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the Consider a simultaneous-move integer game between two players: Marilyn and Noah. Each of player is required to announce a positive integer between 1 to 4. In other words, a player can announce 1, 2, 3, or 4. Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both O. What is Marilyn's maximin strategy? 01 02 03 O
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= a) Suppose x 4 and y = 3. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 1? b) Suppose x = 4 and y = 3. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 2? c) Suppose x = 4 and y = 3. What is the sum of both players' payoffs in all pure strategy Nash equilibria of the game? d) Suppose x = 4 and y = 11. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 1? e) Suppose x = 4 and y = 11. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 2? f) Suppose x = 4 and y = 11. What is the sum of both players' payoffs in all pure strategy Nash equilibria of the game?
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