1. Repeated Game Consider the following normal form game. D Player 1 E F A 10, 10 -12,-1 15, -1 Player 2 B -1,-12 8,8 -1,-1 C -1, 15 -1,-1 0.0 (a) Suppose this game is played once. Find all pure strategy Nash equilibria. (b) Now suppose the game is played two times without discounting. Find all strategy profile that can be played in the first period in a SPNE. (c) Now suppose the game is played 7 times without discounting, where T is a finite number. Find the smallest T such that (E,A) is played in the first period. (d) Now suppose the game is played infinitely many times and the players have a same discount factor 8 < 1. Find the smallest ó that can support the SPNE in which (D,A) is played in every period along the equilibrium path. (Hint: Players use the Grim-Trigger Strategy where (F,C) is used as a punishment).
1. Repeated Game Consider the following normal form game. D Player 1 E F A 10, 10 -12,-1 15, -1 Player 2 B -1,-12 8,8 -1,-1 C -1, 15 -1,-1 0.0 (a) Suppose this game is played once. Find all pure strategy Nash equilibria. (b) Now suppose the game is played two times without discounting. Find all strategy profile that can be played in the first period in a SPNE. (c) Now suppose the game is played 7 times without discounting, where T is a finite number. Find the smallest T such that (E,A) is played in the first period. (d) Now suppose the game is played infinitely many times and the players have a same discount factor 8 < 1. Find the smallest ó that can support the SPNE in which (D,A) is played in every period along the equilibrium path. (Hint: Players use the Grim-Trigger Strategy where (F,C) is used as a punishment).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. Repeated Game
Consider the following normal form game.
D
Player 1 E
F
A
10, 10
-12,-1
15, -1
Player 2
B
-1, -12
8,8
-1,-1
C
-1, 15
-1,-1
0,0
(a) Suppose this game is played once. Find all pure strategy Nash equilibria.
(b) Now suppose the game is played two times without discounting. Find all strategy profile that can
be played in the first period in a SPNE.
(c) Now suppose the game is played T times without discounting, where T is a finite number. Find
the smallest T such that (E,A) is played in the first period.
(d) Now suppose the game is played infinitely many times and the players have a same discount factor
8 < 1. Find the smallest d that can support the SPNE in which (D,A) is played in every period
along the equilibrium path. (Hint: Players use the Grim-Trigger Strategy where (F,C) is used as
a punishment).
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