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, b2 in the first stage as part of an SPNE? Table: SPNE in a repeated game

Managerial Economics: A Problem Solving Approach
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Chapter17: Making Decisions With Uncertainty
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Q30*
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 62 that are needed to support the play of a3, b2 in the first stage as part of an SPNE?
Table: SPNE in a repeated game
2
b₁
b₂
b:3
a1
(10,10)
(2,12)
(0,13)
1
02
(12,2)
(5,5)
(0,0)
az
(13,0)
(0,0)
(1,1)
1) Play of a3, b2 in the first stage cannot be supported as part of an SPNE for any 6₁ and 62 values between 0 and 1.
2) 6₁ ≥ 1/4 and 6₂ ≥ 1/2.
3) 1 1/2 and 62 ≥ 1/4.
4) 81 ≥ 0 and 62 ≥ 1/4.
5) None of the above.
Transcribed Image Text:Q30* 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 62 that are needed to support the play of a3, b2 in the first stage as part of an SPNE? Table: SPNE in a repeated game 2 b₁ b₂ b:3 a1 (10,10) (2,12) (0,13) 1 02 (12,2) (5,5) (0,0) az (13,0) (0,0) (1,1) 1) Play of a3, b2 in the first stage cannot be supported as part of an SPNE for any 6₁ and 62 values between 0 and 1. 2) 6₁ ≥ 1/4 and 6₂ ≥ 1/2. 3) 1 1/2 and 62 ≥ 1/4. 4) 81 ≥ 0 and 62 ≥ 1/4. 5) None of the above.
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