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3SettingupExtraTerritoryCoalitions
In parallel to the spontaneous emergence of unstable coalitions, some extra terri-
tory organizations have been set in the past to create alliances at a global world
level. Among the recent more powerfull ones stand Nato and the former Warsow
pact. These alliances were set above the country level and produce economic
and military exchanges. Each country is then adjusting to its best interest with
respect to these organisations. A variable i accounts for each country i natural
belonging. For coalition A it is i = +1and i = 1for B. The value i =0
marks no apriori. These natural belongings are also induced by cultural and
political history.
Exchanges generated by these coalitions produce additional pairwise propen-
sities with amplitudes {C i,j } . Sharing resources, informations, weapons is basi-
cally profitable when both countries are in the same alliance. However, being in
opposite coalitions produces an equivalent loss. Therefore a pair ( i, j ) propensity
is i j C i,j which can be positive, negative or zero to mark respective coopera-
tion, conflict or ignorance. It is a site induced bond [15]. Adding it to the former
bond propensity yields an overall pair propensity,
J i,j + i j C i,j ,
(7)
between two countries i and j .
At this stage an additional variable β i = ± 1isintroduced to account for
benefit from economic and military pressure attached to a given alignment. It
is still β i = +1for A and β i = 1for B with β i = 0 in case of no pressure.
The amplitude of this economical and military interest is measured by a local
positive field b i which also accounts for the country size and its importance. At
this stage, the sets { i } and i } are independent.
Actual country choices to cooperate or to conflict result from the given set
of above quantites. The associated total cost becomes,
N X
X
H = 1
2
{J i,j + i j C ij i η j
β i b i η i .
(8)
<i,j>
i =1
An illustration is given in Fig. (2) with above exemple of Israel, Syria and Iraq
labeled respectively by 1, 2, 3 with J 12 = J 13 = J 23 = −J and b 1 = b 2 = b 3 =0.
Suppose an arab coalition is set against Israel with 1 = +1and 2 = 3 = 1.
The new propensities become respectively −J + C , −J − C , −J − C . They are
now minimized by η 1 = −η 2 = η 3 to gives an energy of −J − C to all three
couplings.
4ColdWarScenario
The cold war scenario means that the two existing world level coalitions gener-
ate much stonger couplings than purely bilateral ones, i.e., |J i,j | <C i,j since to
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