Question 2 a.) Define a subgame-perfect Nash equilibrium. Consider the following Prisoners' Dilemma stage game: 1 U D 2 6 L 12 6 1 1 4 R 12 4 b.) What is the subgame-perfect Nash equilibrium when the stage game is repeated twice? Now assume that the stage game is repeated an indefinite number of times, with a continu- ation probability & € (0, 1) at the end of every period. c.) Describe the trigger strategy for each player that induces cooperation on (U, L). d.) * For what values of d are these trigger strategies a subgame-perfect Nash equilibrium? e.) Explain intuitively why the indefinite nature of the interaction helps cooperation.

Question 2 a.) Define a subgame-perfect Nash equilibrium. Consider the following Prisoners' Dilemma stage game: 1 U D 2 6 L 12 6 1 1 4 R 12 4 b.) What is the subgame-perfect Nash equilibrium when the stage game is repeated twice? Now assume that the stage game is repeated an indefinite number of times, with a continu- ation probability & € (0, 1) at the end of every period. c.) Describe the trigger strategy for each player that induces cooperation on (U, L). d.) * For what values of d are these trigger strategies a subgame-perfect Nash equilibrium? e.) Explain intuitively why the indefinite nature of the interaction helps cooperation.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 2
a.) Define a subgame-perfect Nash equilibrium.
Consider the following Prisoners' Dilemma stage game:
2
R
1
12
U
1
1
4
D
12
4
b.) What is the subgame-perfect Nash equilibrium when the stage game is repeated twice?
Now assume that the stage game is repeated an indefinite number of times, with a continu-
ation probability 8 E (0,1) at the end of every period.
c.) Describe the trigger strategy for each player that induces cooperation on (U, L).
d.)
*
For what values of d are these trigger strategies a subgame-perfect Nash equilibrium?
e.) Explain intuitively why the indefinite nature of the interaction helps cooperation.

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Step 1: Define Prisoner's Dilemma

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Step 2: Define SPNE

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Step 3: Detect SPNE in given payoff structure

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Step 4: Describe the trigger strategy

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Step 5: Solve for delta

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Step 6: Explain for (e)

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