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new explanation is given in Section 6 to Eastern European instabilities following
the Warsaw pact dissolution as well as to Western European stability. Some
hints are also obtained on how to stabilize these Eastern Europe instabilities.
Last Section contains some concluding remarks.
2PresentationoftheModel
We start from a group of
N
independant countries [12]. From historical, cultural
and economic experience, bilateral propensities
J
i,j
have emerged between pairs
of countries
i
and
j
. They are either favoring cooperation (
J
i,j
>
0), conflict
(
J
i,j
<
0) or ignorance (
J
i,j
= 0). Each propensity
J
i,j
depends solely on the pair
(
i, j
) itself. Propensities
J
i,j
are local and independant frozen bonds. Respective
intensities may vary for each pair of countries but are always symmetric, i.e.,
J
ij
=
J
ji
.
From the well known saying “the enemy of an enemy is a friend” we get the
existence of only two competing coalitions. They are denoted respectively by A
and B. Then each country has the choice to be in either one of two coalitions. A
variable
η
i
where index i runs from 1toN, signals the
i
actual belonging with
η
i
= +1for alliance A and
η
i
=
−
1for alliance B. From bimodal symmetry all
A-members can turn to coalition B with a simultaneous flip of all B-members to
coalition A.
Given a pair of countries (
i, j
) their respective alignment is readily expressed
through the product
η
i
η
j
. The product is +1 when
i
and
j
belong to the same
coalition and
−
1otherwise. The associated “cost” between the countries is mea-
sured by the quantity
J
ij
η
i
η
j
where
J
ij
accounts for the amplitude of exchange
which results from their respective geopolitical history and localization.
Here factorisation over
i
and
j
is not possible since we are dealing with
competing bonds [15]. It makes teh problem very hard to solve analytically.
Given a configuration
X
of countries distributed among coaltions A and B, for
each nation
i
we can measure its overall degree of conflict and cooperation with
all others
N −
1countries via the quantity,
N
X
E
i
=
J
ij
η
j
,
(1)
j
=1
where the summation is taken over all other countries including
i
itself with
J
ii
≡
0. The product
η
i
E
i
then evaluates the “cost” associated with country
i
choice
with respect to all other country choices. Summing up all country individual
“cost” yields,
N
X
E
(
X
)=
1
2
η
i
E
i
,
(2)
i
=1
where the 1
/
2 accounts for the double counting of pairs. This “cost” measures
indeed the level of global satisfaction from the whole country set. It can be recast
as,
