Consider the stage game shown in Table "SPNE in a repeated game". Suppose this game is played twice. What are the minimum values of d1 and 82 that are needed to support the play of a3, b1 in the first stage as part of an SPNE?

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Q29
Consider the stage game shown in Table "SPNE in a repeated game". Suppose
this game is played twice. What are the minimum values of 8₁ and 82 that are
needed to support the play of a3, b₁ in the first stage as part of an SPNE?
Table: SPNE in a repeated game
2
b₁
b₂
b3
α1
(10,10)
(2,12)
(0,13)
1
a2
(12,2)
(5,5)
(0,0)
az
(13,0)
(0,0)
(1,1)
1) Play of a3, b₁ in the first stage cannot be supported as part of an SPNE
for any 6₁ and 62 values between 0 and 1.
2) 1
1/4 and 82 ≥ 1/2.
3) 1 ≥ 1/2 and 8₂ ≥ 1/4.
4) 81 ≥ 0 and 82 ≥ 1/4.
5) None of the above.
Transcribed Image Text:Q29 Consider the stage game shown in Table "SPNE in a repeated game". Suppose this game is played twice. What are the minimum values of 8₁ and 82 that are needed to support the play of a3, b₁ in the first stage as part of an SPNE? Table: SPNE in a repeated game 2 b₁ b₂ b3 α1 (10,10) (2,12) (0,13) 1 a2 (12,2) (5,5) (0,0) az (13,0) (0,0) (1,1) 1) Play of a3, b₁ in the first stage cannot be supported as part of an SPNE for any 6₁ and 62 values between 0 and 1. 2) 1 1/4 and 82 ≥ 1/2. 3) 1 ≥ 1/2 and 8₂ ≥ 1/4. 4) 81 ≥ 0 and 82 ≥ 1/4. 5) None of the above.
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