7 Q29Consider the stage game shown in Table "SPNE in a repeated game". Supposethis game is played twice. What are the minimum values of 8₁ and 82 that areneeded to support the play of a3, b₁ in the first stage as part of an SPNE?Table: SPNE in a repeated game2b₁b₂b3α1(10,10)(2,12)(0,13)1a2(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 SPNEfor any 6₁ and 62 values between 0 and 1.2) 11/4 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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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?

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?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter19: Externalities And Public Goods

Section: Chapter Questions

Problem 19.12P

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Question

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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