Peter Rabbit Mr McGreggor C B 0, h 1,1 C 3,3 B h, 0 Suppose the one period game is repeated infinitely and that the both Peter Rabbit and Mr. McGreggor discount using 8 € (0, 1). (a.) Specify a grim trigger strategy which if played by both players would result in cooperation each period, and where the punishment for choosing B is reverting back to the Nash Equilibrium of the static game for every subsequent period. Make sure that the strategy is well specified. (b.) Let h=5. For what range of 8 does the strategy specified in (a.) form a SPNE when played by both players? Show your work. (c.) Now let 6. For what range of h does the strategy specified in part (a.) form a SPNE when played by both players? Show your work.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter2: Solving Linear Inequalities
Section: Chapter Questions
Problem 1CT
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Peter Rabbit and Mr. McGreggor have come up with a deal where Peter gets a
small piece of carrot every day in exchange for not breaking into Mr. McGreg-
gor's garden, and Mr. McGreggor does not build a fence. So the choices for each
are either C (cooperate) or B (Build Fence) or (Break in). The simultaneous
game for a single period is displayed below. Note: h> 3
Peter Rabbit
Mr McGreggor
C
B
C 3,3 0, h
B h, 0 1,1
Suppose the one period game is repeated infinitely and that the both Peter
Rabbit and Mr. McGreggor discount using 8 € (0, 1).
(a.)
Specify a grim trigger strategy which if played by both players would
result in cooperation each period, and where the punishment for choosing B is
reverting back to the Nash Equilibrium of the static game for every subsequent
period. Make sure that the strategy is well specified.
(b.)
Let h=5. For what range of 8 does the strategy specified in (a.)
form a SPNE when played by both players? Show your work.
(c.)
Now let d = 3. For what range of h does the strategy specified in
part (a.) form a SPNE when played by both players? Show your work.
Transcribed Image Text:Peter Rabbit and Mr. McGreggor have come up with a deal where Peter gets a small piece of carrot every day in exchange for not breaking into Mr. McGreg- gor's garden, and Mr. McGreggor does not build a fence. So the choices for each are either C (cooperate) or B (Build Fence) or (Break in). The simultaneous game for a single period is displayed below. Note: h> 3 Peter Rabbit Mr McGreggor C B C 3,3 0, h B h, 0 1,1 Suppose the one period game is repeated infinitely and that the both Peter Rabbit and Mr. McGreggor discount using 8 € (0, 1). (a.) Specify a grim trigger strategy which if played by both players would result in cooperation each period, and where the punishment for choosing B is reverting back to the Nash Equilibrium of the static game for every subsequent period. Make sure that the strategy is well specified. (b.) Let h=5. For what range of 8 does the strategy specified in (a.) form a SPNE when played by both players? Show your work. (c.) Now let d = 3. For what range of h does the strategy specified in part (a.) form a SPNE when played by both players? Show your work.
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