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Fighting to Win: Translating Military Gains into Political Victories
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| | Unformatted Document Text:
9
where 05
.
0
=
=
d
a
α
α
,
1
1
1
=
=
d
a
θ
θ
, and
05
.
3
3
2
2
=
=
=
=
d
a
d
a
θ
θ
θ
θ
. Note that both utility
functions are concave in resources. This implies that the loss in utility resulting from a given
resource loss rises as the amount of resources falls – each country is more sensitive to resource
losses as the war continues.
Simulation 1. Base Case
We start from a base case with the following parameters:
20
=
a
B
,
20
=
d
B
,
5
=
a
R
, and
5
=
d
R
. Each victory costs a player one unit of resources and each loss costs the player one and a
half units of resources, so
4
=
w
a
R
,
5
.
3
=
l
a
R
,
3
=
ww
a
R
,
5
.
2
=
wl
a
R
, etc. In the base case there are
five types of D,
}
60
.
55
,.
50
,.
45
,.
40
{.
}
,
,
,
,
{
5
4
3
2
1
=
d
d
d
d
d
, and A’s priors have a uniform
distribution,
}
5
1
,
5
1
,
5
1
,
5
1
,
5
1
{
}
,
,
,
,
{
5
4
3
2
1
=
λ
λ
λ
λ
λ
.
Note in the base case both players have benefits of the same size and the same level of
resources, and if A fought a battle with the average defender then A would win with probability
.5. In the base case in equilibrium A is not willing to attack in stage 1 so she cannot make a
credible demand. In this instance, war never starts. In what follows, we consider the effects of
changing the parameters on the equilibrium. The outcomes of conflict are to some extent random
simply because battle outcomes are random, and this implies that the same initial underlying
conditions can lead to a variety of outcomes. We describe all of the possible outcomes in each
case. For the sake of brevity, we do not describe how A’s beliefs evolve over the course of the
conflict – we restrict our attention to how proposals and D’s behavior changes. However, we will
describe how to compute A’s ex ante beliefs about the likelihood of settlement in each stage.
Simulation 2. Distribution of Power and Benefits
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| | Authors: Werner, Suzanne. |
|
| |
|
|
9
where 05
.
0
=
=
d
a
α
α
,
1
1
1
=
=
d
a
θ
θ
, and
05
.
3
3
2
2
=
=
=
=
d
a
d
a
θ
θ
θ
θ
. Note that both utility
functions are concave in resources. This implies that the loss in utility resulting from a given
resource loss rises as the amount of resources falls – each country is more sensitive to resource
losses as the war continues.
Simulation 1. Base Case
We start from a base case with the following parameters:
20
=
a
B
,
20
=
d
B
,
5
=
a
R
, and
5
=
d
R
. Each victory costs a player one unit of resources and each loss costs the player one and a
half units of resources, so
4
=
w
a
R
,
5
.
3
=
l
a
R
,
3
=
ww
a
R
,
5
.
2
=
wl
a
R
, etc. In the base case there are
five types of D,
}
60
.
55
,.
50
,.
45
,.
40
{.
}
,
,
,
,
{
5
4
3
2
1
=
d
d
d
d
d
, and A’s priors have a uniform
distribution,
}
5
1
,
5
1
,
5
1
,
5
1
,
5
1
{
}
,
,
,
,
{
5
4
3
2
1
=
λ
λ
λ
λ
λ
.
Note in the base case both players have benefits of the same size and the same level of
resources, and if A fought a battle with the average defender then A would win with probability
.5. In the base case in equilibrium A is not willing to attack in stage 1 so she cannot make a
credible demand. In this instance, war never starts. In what follows, we consider the effects of
changing the parameters on the equilibrium. The outcomes of conflict are to some extent random
simply because battle outcomes are random, and this implies that the same initial underlying
conditions can lead to a variety of outcomes. We describe all of the possible outcomes in each
case. For the sake of brevity, we do not describe how A’s beliefs evolve over the course of the
conflict – we restrict our attention to how proposals and D’s behavior changes. However, we will
describe how to compute A’s ex ante beliefs about the likelihood of settlement in each stage.
Simulation 2. Distribution of Power and Benefits
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