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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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