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Learning to Consolidate Democracy
Unformatted Document Text:  39 What offer will provide an incentive for R types to separate? We begin by backwards inducting on R’s decision problems in the first and second period. In the second period R accepts (1-b 2 ), where 1-b 2 = R H if: 2 2 2 (1 ) 1 1 H H H b R R b R b δ δ δ − ≥ − ≥ − ≥ and R rejects (b 2 ) if: 2 2 2 (1 ) 1 1 H H H b R R b R b δ δ δ − < − < − < In the first period R accepts (b 1 ) where 1-b 1 =R L if: 2 1 2 1 2 1 2 1 2 1 2 1 1 2 (1 ) 1 1 [ 1 ]* 1 1 1 ( 1) 1 ( 1) 1 b b b b b b b b b b b b b b δδ δ δ δ δ δ δ δ δ δ − ≤ − − ≤ − − − ≤ − − − + + ≥ − + ≥ − + ≥ ≤ − + R rejects b 1 if: 2 1 2 1 2 1 2 1 2 1 2 1 1 2 (1 ) 1 1 [ 1 ]* 1 1 1 ( 1) 1 ( 1) 1 b b b b b b b b b b b b b b δδ δ δ δ δ δ δ δ δ δ − > − − > − − − > − − − + + < − + < − + < > − +

Authors: Casper, Gretchen. and Joyce, Kyle.
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39
What offer will provide an incentive for R types to separate? We begin by backwards
inducting on R’s decision problems in the first and second period.
In the second period R accepts (1-b
2
), where 1-b
2
= R
H
if:
2
2
2
(1
)
1
1
H
H
H
b
R
R
b
R
b
δ
δ
δ
− ≥
and R rejects (b
2
) if:
2
2
2
(1
)
1
1
H
H
H
b
R
R
b
R
b
δ
δ
δ
<
− <
<


In the first period R accepts (b
1
) where 1-b
1
=R
L
if:
2
1
2
1
2
1
2
1
2
1
2
1
1
2
(1
) 1
1
[
1
]* 1
1
1
(
1) 1
(
1) 1
b
b
b
b
b
b
b
b
b
b
b
b
b
b
δ
δ δ
δ δ
δ δ
δ
δ
δ
δ
≤ −
≤ −
− ≤ −
− +
+ ≥
− + ≥
− + ≥
− +

R rejects b
1
if:
2
1
2
1
2
1
2
1
2
1
2
1
1
2
(1
)
1
1
[
1
]* 1
1
1
(
1) 1
(
1) 1
b
b
b
b
b
b
b
b
b
b
b
b
b
b
δ
δ δ
δ δ
δ δ
δ
δ
δ
δ
> −
> −
− > −
− +
+ <
− + <
− + <
>
− +


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