Dissolution of a Global Alliance
3 Dissolution of a Global Alliance
Produced by the polarization of countries ’ interests through their natural belongings , the global alliances lead to emergence of new propensities between the countries , which generate stability for particular amplitudes . Once the stability is achieved , the system remains stable for some time — in reality , political , economic , or other interests and motivations are not static , they are subject to evolutionary changes .
When those propensities change , completely or partially , they may exhaust the incentive effect of a global alliance putting the respective countries , for which the stability prevailed during the existence of the alliance , back to their primary geographic-ethnic bonds . Depending on the distribution of the attraction to the global alliance and the amplitudes of the globally induced interactions , the associated coalition exhibits different effective resistance to the dissolution — the robustness of the stability that prevailed during the existence of the alliance .
Formally , the weakening of a global alliance is the weakening of the respective natural belonging parameters of countries by some multiplier α ∈ [ 0 , 1 ]. The total dissolution takes place when α = 0 , which sets the natural belonging parameters to zero .
The weakening of global alliance , being generally a dynamic process , should be expressed in terms of dynamic weakening parameter α ( t ), which is a continuous or discontinuous function of time . The weakening introduces a dynamical aspect into the initially unchanged model in which changes of the primary propensities are negligible .
Definition 1 ( Weakening of a Global Alliance ). Given two actors i , j and global alliance M that descends , assume without loss of generality that actor i naturally belongs to the global alliance M . Then , the weakening of the alliance is expressed through the following change of the actors ’ mutual propensity :
p ij
total
( t ) = J ij + ε i
ε j
G ij α i ( t )
( 8 )
The robustness of the stability is naturally determined by the proximity of the new interaction amplitudes to the boundaries of the stability space . We can conclude from Formula ( 8 ) that while stability depends on the sign of the total propensity , its robustness depends on the value of the additional , externally induced propensity G ij
.
It can be observed from Formula ( 8 ) that , taken for all the pair of countries , leaving the closed area of the stability space is always abrupt . This fact explains that in reality , dissolution tends to be followed by unexpected and brutal bursts of conflict .
In this work , we consider the system to be at a moment t of the weakening process of the alliance where the system is out of its stability space — the alliance dissolves when the competitive ( negative ) circles re-appear in the system . On the way , before the system reaches the dissolution , transitional stable coalitions are possible while the system is still in the stability space .
4 Two Cases of Dissolution
We focus here on the dissolution
of a global alliance that has previously created stability . When the dissolution occurs , the incentive effect of the initial global concept vanishes for this particular alliance . This makes the negative circuits of the primary propensities between the respective countries to be again instrumental in their respective search for optimization .
Two different effects of the dissolution can be distinguished : ( 1 ) the instability
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