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Underfunding in Terrorist Organizations
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In the constrained case,
is decreasing in
c when M does not want to skim.
Unfortunately, because
p
0
d
dp
γ
has indeterminate sign for the same reasons that (8) does,
we cannot sign the change in the cutoff between the honest and skimming regimes.
Moving on to b , we have:
0
2
(1
)
M
dw
db
b
γ
γ δ
∗
−
=
, (15)
2
(1
)
M
dx
db
b
γ
γ δ
∗
−
=
. (16)
Both of these are positive for
12
p
> , so that, in line with our intuition, the more M
cares for money, the more M skims, forcing B to pay more. We also note that these
derivatives are true for all
, and that
p
0
dw
dx
db
db
∗
∗
=
, implying that B simply replaces the
extra money lost to skimming when rises; the outcome remains the same.
Accordingly, greedier agents do not reduce the probability of success, as long as B’s
wealth is sufficiently high.
b
In the constrained case, since M’s actions are set,
does not depend on b and
the success probability is again constant in b ; however, the range over which M
would not want to skim does depend on M’s attributes. The higher b is, the lower
p
0
γ
gets, implying less greedy agents begin to skim as increases. This fits our intuition
as b effectively represents the marginal utility of skimming.
b
The results for
γ are:
0
2
1
M
dw
d
b
γ
γ δ
∗
=
, (17)
29
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| | Authors: Shapiro, Jacob. and Siegel, David. |
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|
In the constrained case,
is decreasing in
c when M does not want to skim.
Unfortunately, because
p
0
d
dp
γ
has indeterminate sign for the same reasons that (8) does,
we cannot sign the change in the cutoff between the honest and skimming regimes.
Moving on to b , we have:
0
2
(1
)
M
dw
db
b
γ
γ δ
∗
−
=
, (15)
2
(1
)
M
dx
db
b
γ
γ δ
∗
−
=
. (16)
Both of these are positive for
1
2
p
> , so that, in line with our intuition, the more M
cares for money, the more M skims, forcing B to pay more. We also note that these
derivatives are true for all
, and that
p
0
dw
dx
db
db
∗
∗
=
, implying that B simply replaces the
extra money lost to skimming when rises; the outcome remains the same.
Accordingly, greedier agents do not reduce the probability of success, as long as B’s
wealth is sufficiently high.
b
In the constrained case, since M’s actions are set,
does not depend on b and
the success probability is again constant in b ; however, the range over which M
would not want to skim does depend on M’s attributes. The higher b is, the lower
p
0
γ
gets, implying less greedy agents begin to skim as increases. This fits our intuition
as b effectively represents the marginal utility of skimming.
b
The results for
γ are:
0
2
1
M
dw
d
b
γ
γ δ
∗
=
, (17)
29
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