Policy and Complex Systems
direction ε i
ε j and favors either cooperation or conflict .
The overall propensities between the countries , including both the historical inclinations and the new globally induced propensities , are determined as follows :
p ij
= J ij + ε i
ε j
G ij
Respectively , the net gain of actor i is
H i
= S i
∑ j≠i
( J ij + ε i
ε j
G ij
) S j
( 3 )
( 4 )
In the presence of external incentives of the global alliances , the countries ’ associations into coalitions are adjusting with regard to the new propensities , bringing in a planned feature into the coupling with respect to the spontaneous interactions based on the primary historical propensities .
2.3 Stabilization by Factors of Interest
When referring to the system of countries , a precise factor of countries ’ interest produces particular dispositions to the present global alliances . Those dispositions determine the countries belonging to the alliances and encourage the new exchanges aligned with that factor . The appropriate amplitudes of the exchanges produce a uni-factor stabilization of coalitions among the countries .
Given two opposite global alliances M and C and the active factor of countries interests G that produce the countries ’ belonging parameters { ε } 1 N , the globally induced propensities are p ij total
= J ij + ε i
ε j
G ij
.
In real cases , several factors of countries ’ interests can be active to the global concept — along with religious concerns ; the concept may impact economical , ecological , moral , political , and other interests . Accordingly , distinct interests simultaneously influence the interactions between the countries in different ways by inducing specific interactions . The appropriate amplitudes of the exchanges produce the multi-factor stabilization of coalitions among the countries .
Given two active factors of countries ’ interests G and K producing the respective belonging parameters { εi } 1
N and
{ βi } 1
N globally induced propensities are generated as follows :
total
p ij
= J ij + ε i
ε j
G ij
+ β i
β j
K ij
G K
= J ij + p ij
+ p ij where
G
ε i
ε j
G ij
≡ p ij
and β i
β j
K ij ≡
p ij
K
( 6 )
The general multi-factor case can be represented , with no restriction on the generality , through the two-factor form : one of the factors unifies the amplitudes of all the positive new coupling and the other unifies those of all the negative ones . According to Equation ( 2 ), the stability terms read as follows :
A system is stable if and only if for any circle Ω in the system ,
Π i , j Ω
p ij
total
≥ 0
∈
( 7 )
Stability space is defined to be a set of all the globally induced interactions
{( G ij , K ij
)} i , j such that the effective propensities p ij
G , K satisfy the above stability condition .
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