Consider the following stage game: L C T 7,6 11,5 M 5,10 9,9 Suppose that the game is repeated infinitely many times. Player one (choosing between T and M) has discount factor 1, while player 2 has discount factor 82. Consider the following strategy profile for the game: • Player 1: Play M in the initial period; in subsequent periods, keep playing M as long as (M,C) was the outcome in every previous period; otherwise, play T. • Player 2: Play C in the initial period; in subsequent periods, keep playing C as long as (M, C) was the outcome in every previous period; otherwise, play L. What is the condition on the discount factor of Player 2 such that this strategy profile can be a SPNE? (a) 2 ≥0 (b) 82₂ ≥ 1/ (c) d₂ ≥ (d) §₂ ≥ 1/1 2 (e) d₂ ≥ 31 4
Consider the following stage game: L C T 7,6 11,5 M 5,10 9,9 Suppose that the game is repeated infinitely many times. Player one (choosing between T and M) has discount factor 1, while player 2 has discount factor 82. Consider the following strategy profile for the game: • Player 1: Play M in the initial period; in subsequent periods, keep playing M as long as (M,C) was the outcome in every previous period; otherwise, play T. • Player 2: Play C in the initial period; in subsequent periods, keep playing C as long as (M, C) was the outcome in every previous period; otherwise, play L. What is the condition on the discount factor of Player 2 such that this strategy profile can be a SPNE? (a) 2 ≥0 (b) 82₂ ≥ 1/ (c) d₂ ≥ (d) §₂ ≥ 1/1 2 (e) d₂ ≥ 31 4
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the following stage game:
L
C
T
7,6 11,5
M 5,10 9,9
Suppose that the game is repeated infinitely many times. Player one (choosing between T
and M) has discount factor 1, while player 2 has discount factor 82. Consider the following
strategy profile for the game:
• Player 1: Play M in the initial period; in subsequent periods, keep playing M as long
as (M,C) was the outcome in every previous period; otherwise, play T.
• Player 2: Play C in the initial period; in subsequent periods, keep playing C as long as
(M, C) was the outcome in every previous period; otherwise, play L.
What is the condition on the discount factor of Player 2 such that this strategy profile can
be a SPNE?
(a) 2 ≥0
(b) 82₂ ≥ 1/
(c) d₂ ≥
(d) §₂ ≥ 1/1
2
(e) d₂ ≥ 31
4
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