Military Power influences Economoic Cooperation . 1. Jörg Hermanns: ... bility criteria (crisis stability, arms race stability, cost effectiveness) the «lynamic behavior of the model can be ... and conflicts (especially the greenliouse problem).
IMSTTTUT
FOR
ANGEWANDTE WSTEMFOLSCHUNG UND QPEbA'TIQHi$TBUEAWH
Inhaltsverzeichnis
Vorwort von Prof. Dr. Reiner K. Huber Inhaltsveneichnis
Vladirnir Akimov, Omed Ischebek, Mikhail Khaiztiikov, Götz Neuneck: Modeling Arms Races with Diplomatie Tnteractions .....................................
1
Doris A~iitaBehreru: A Two-dimensional Model on the Arms Race: StabiIity and Conmol ef Chaotic Motion ...............................................
19
Bj@rttEbbese~z: A DifTerentiaI Game Form Model of Interacting Nations
-
Military Power influences Econornoic Cooperation .................................... 33
Jörg Hemanm: Erkennung funktionaler Zusammenhänge in detaiIIierten Konfliksimulationsrnodellen ..........................................................
45
Markus Juthe: Occurence of Chaos in a Model of InternationaI Security ...............................
65
Otj+ied 1schl.hek: Tactical Nuclear Weapons of NATO Modeling German-American Relations under the Strategy of FlexibIe Response ........ 79 Rolatid Reimers: Seismic Verification of a Nuclear Test Ban: A Mathernatical Approach .... „, ................. . .. . . . . . . . . . . . . . . . . . - . . . . . . . . 95
J ü r ~ e nScht'ffrati: Modelling International Security Problems in the Frarnework of the SCX Model ...... I03 Andreas Tolk, K l a u Helling:
Quasineural Prograrnming of Fuzzy Con~ollers.......................................
121
Modelling International Security Problems in the Framework of the SCX Model
Abstract
The C CX iiiodel describes t he coupled. rionlinear and tinie-discrete in teraction between goals (e.g. security. siistainability) S , rtieans (resoiirces, costs) T* and rdevant systern variables .Y of t h e systein for varioi~sactors. The rlynat~iics is driven by the goal fi~nction,which is defined as tlie ~ x p e c t e d~iayoffi r i a game itiatrix. and tla~ripenedZ>y tlic available nieans. .-lccortling to tliffereiit stal~ilitycri teria (crisis s tahility, arrns rare stability. cos t ~ffectiveness)t he d yna~ziic Iiehavior of the itiode? can be exailiined. Xpplications of the S I ' S iiiotltl incliirle: The interplay lietween the Iiiiildup a n d reduction of strategic nuclear weapons, defense systerris and coiin ternieasures; in teraction between proliferation, tilissile defenses nnd international controls of arrriament and technology;
m t he
e
the iitipact ef changes in tEie tvorld energy system ou Pcononiy, ~iivironiiicnt and conflicts (especially tlie greetihouse probletti ) Zusammenfassung
Mit tlriii SC:S I\iorlell lasseii sich g r k o p p ~ l t ~tiichtlj~ieai-r , i i i i r l z r i t t f i s k i ~ t111~ teraktionen zrviscbeii Zielen ( C ) , Rcsourc~n/Kosteri (I:)iintl rrlcvarit~nS~sterrivariablen ( X ) fiii- unterschiedliclist~Akteure abbildcri. Dabei liegt tler Dynaiiiik des Systeiiis eine Zielfiinktion in Fot-111 des ~ r w a r t e t e nGewinns ciiier sl)ielt~~atrix zti C;runtle. .Je nach Definition tler Ziele. - ztiliieist iiriterscliiedliclie -4spekt~. der Sicherheit - reagiert das Systeni entsprechentl iinrl kann soniit tin tersiiclit werden. Anwendiingen dieses rllnsat zes schlieflen U . a. folgende Aspekte ein i
I
die Zusaiaiiiienhänge zwischea !l iif- irntl Aliriis tiing ini riiiklearen B~rricli. der V~rteicEigungssyst~rne sowie der Ergreifting soiistiger C;~geiiiiiaßiialiirieri:
die RoUe der Proliferation, llaketenabwehr tind rler internationalen Rüsti~ngskontrolle: der Einfliiß ökonoitijsclier itntl ökologisch~rFaktoren.
J. Scheffran
1
Basic Variables and Equations
The growirig teridency towards cor-tiplexity, i~istability arid u~icertaiiityi 11 i titernatiorial security is analyzed wi thin t he framework of a nonlinear arid tinie-cjiscrete dyriainjc rnodel, caIled the SCX niodel.' It describes the iiiteraction between goals Aqj ((e.g. Semrity, sustainabili ty), nieans Ci(resources, costs), aud relevant st ate variables X i (e.g. rnilitary c.apalitities, energy coiisump tioii, environrnerltal polu tiori) for several actors i = 1, ..., n (e.g. ~iatiotis).~ All variabies can vary with time i . 1. The systern variables ,Yk;(f) ( b = 1, ...,tn) represe~itthe essential ser.urityrelevaiit variables, e.g. politicai, ecologica1, econoinic atid mihtary factors, wliicb can be cornprised iii tlie state vector .pi(t)= (Xii(t),..., -Yvai(t))s
2. The costs Cz(t)= C',"=, c k ; A X k i ( t )are a ineasure for the resources speiit at time t to iriduce state transitions &Gi(f)= X k i ( i + I ) - Xki(tj. cki are t!ie costs per
unit of A.Yk;(t). 4
4
:3. The security fitiictioii ,Si(Xl ( t ) ,..,Ali:,(t))(i = I , .... FL) i s a ~ ~ t i l i111easi11-e ty for t b ~ expected payoff (gaiiis tiiiiius losses) of differeiit optioiis. clepending oii tlie state vectors z;(t)of eacli side '.i
CEianges -+ iii security ALSiare deterrziiried by tlie chalige i i i secilrity relevant capttbilities Xj of ariy side j . Tlie basic reIatiorlship iii the cirigle-actor, siagle-variable case is AS = s. AX = s c - I:, where A arid C are tbe tlaargilial serurity ~ffectsarid the tiiargirisl costs. sc 5 s/c is called thr security-rost effec.t. For ti~ultiplractors atid niultiple variables, tiie directio~isof tbe v ~ c t o r sX$i tiavc to be considerecl for sc. Tlie deviatioii frotli tlie state of adequate (sufficieiit) security ,Si = 0 aiid the security cliaiiges Ac;i are drivirlg forces for tlie cliatiges i ~ ttie i aunual budget. tri order to describe tlic cliariges of these variables for eadi actor i , the following iiotiliriear. tiiiie-(Iiscrete differerice equatiotis are ricecl ( 1 i s iiiostly igiior~diii tlie follui~iiig).~
"he SC:X model is a framework whicli is based o n and integrates different approachcs of arnis race models deveioped by L.F. Richardson, h1. Intriligator, A . Saperstein, C;. Xlayer-lirms, s. Cirossmann, S. ßrarns, B. O'Neill. For details of the SCX model and retated literatiire see [ScheF89]. 'In the following 5 and wiil be simply callecl "security" and "costs", ivithout giving s p ~ c i f i r units. 31t must Lie rioted that seciiiity not necessarily represetits generalty agreeri '"ositive" values Iiut descrities r n o t i v ~ sand inteiests of the r~speckiveactors which can be Seen as "negative" or aggressiv^ by other actors. 4 A always repsesents tlie ctiange in a variable Iietwwn trvo time steps 1 lind t 4- I , for exarnpl~, A.Si(t) = Si(t 1) S i ( £ ) .
+ -
Modellinserv~d.
-
Tlie i w t o r A.Y, is restricterl liu tbe r-osts,'C nvaiIabl(x at ,z c-ertaiii tiiiir itticl tlie iiiiit rosts rb,r,. Its directioii carl IIP rI10se11 freely iyitllitl tlie rost roristrsitit hy defi~iiiigthe fractio~isfk, s p p n t foi. pacli varialile .Yki, \r.liicli rsseiitially I Irt~ririiiit.11ie src.iiri~~'-4-ost effects:'
4
4
f
Tliese itic,lude the inargiiia1 security effects -5;; = l . q i i l , sij = lsijj of tlw vectors .sii = (SI;;,.... .5,iiii), ~ i = j (.slij, ..., siriij) ~vitlithe iriargi~ialsecurity effects .f;k;j ==: il,$,/i-l,Yk, (for siiiall .Ykj), the margirial costs C; = I(cli, .... c,,,i)I and tlie djrection aiigles Q i i , Qji, fli bettt.eeii tlie changes AX; aiid t he vectors . Lu t a~>pronriirs1 for Iiigli approxiiiiately proportioiial ivi tli j's iiiceiiti w to act first S j F . These requireiiieiits cari be fulfilled I>p
,'?Y
% ~imilarfunction has been defined Iiy [BraXB] for strategic ivarfare. "irnilar measiires have Iwm rlefined liy [C:a182J.
with tlie properties $(0) = 0,~1$(rn) = I. Cornbiiiiug bat11 aspects provides a lirriit condition betweeii preeiiiption and non-preemp tion, F pji
-
-q
sy F + ,sjS
- l'jF* - ,?:F + s,!S -
3
whidi fiiially leada to tlie coiiditioti (S:F.~iF)/ (S:"S?) = 1.
Definition: The crisis instability index is defined as
A strategic situatiotl is called c m s k unstable for G I S > 1 ( C R I S > 0).
Remark: C I S is closely coliiiected to the crisis iristability iiidex whicll Iias Liee~iderived iri a different, iiiore axio~iiatictvay by B. Q'NeiIIbn In the case C I S > 1 tlie product of iiiceiit ives for preeiiiytiug exceeds tlie product of iticeiitives for wai tiug, corresporidiiig to crisis iristability. CI.'? < 1 corresporids to a situatioii whicli is iilore crisis stable, because ilori-preeniption is optimal for both sides. The t hreshold case C I S = I ( C R I S = 0) correspoiids to tlie liiiiit coiiditioii betweeii preeiiiptioii arid non-preemptioii = wliicli leads to
tlieii tlir siti~atioii Tlius. if oiie side is pwceiwd to yreeiiipt witli probability beconies crisis uiistable, if t he otlier side. is expected to preeriipt with proliability =1 3t
Arms race stability Aiialysis of the SCX iiiodel suggests the defi~iitioiiof ari iridex of arilis race instability betweeri two ac.tors:" 'See {O'Nei87], who used this measure to estimate the stabilizing or destablizing etTect of strategic defense systems, compared with other options. D s p i t e critical comments in' [Fich86], PIS is a usefiil rneasure to rnodel the interaction lietween preemption probaliilities and payoffs between WO actors. To include caces with negative incentivm, t t i - tiiodified crisis instability index can be defined as the differente CRIS = ( I ,5{F)(1+ (1 + ,,':$)(1+ ,gS). C;IS or C:RIS can Iie generalised to any game theoretic problern to model the switching between options. 9A derivation of this index, partly based on linear stability analysis, is given in [ScheMS], Chapter 12. Since the security-cost caefficients scij may be Zero or even negative, one can define a rnodifietl arrns race instability index ARiS = (1 acia)(I SC^^) ( I sci ,)(I SC?^).
+
$iF) -
+
+
- +
+
Mudelljnq I,irernarionul Securip Problems
SC12 SC21
AIS
.5C11SC22
= CERi.CER -
irr
rhe Ftumework of rhe SCX Model
ASI2
as„1 1 , ~ ~ ~ '
where CER; = Ci/C3= sci,/scii is the cost-sccurity-esctiang~:ratio to achieve ASi = 0, A I S is tlie ratio of the exterrial security effects iriduced by the oppoiierit aad the inter~ialsecurity effects of the owii activities. Tlie inverse ratio 0 = 1/AI,C Iias been used as ati iridex of arliis race stability. A I S = 1 represeiits a lirnit coiiditioti for security-cost-effectiv~11ess, giveri by CERi. For A I S > 1 tlie costs of hoth sides iiiduce a mutual reduction in security, sirice the product of tlie security losses ASij = scijC;; produced Iiy t he oppoiie~itexceed t he self-i~lducedsecuri ty gairis ASi; = - ~ G ~i~1iicti G, niust be coinpensat~dby ari iricrease in costs, leadi~igto a furtlier reductiori i ~ seczirity i (escalatiotl). A I S < 1 corresponds to arms race stability. (:lose to the limit case AI,? = 1 (or iri its imriiediate vicinity) other pararneters. i i i particular ri and ki cari Eead to irregular, cliaotic beliavior, destroying predictabiIity.1° 111 tlie co~itextof tlie SCX i~iodeltlir followi~igq i r ~ s t i o n srari be exa~nitiecI:" How cari, with a giveii securitv fiirictiori Si, the ctynaiiiirs lie iirflueiired way tliat is in tlir s t a b l ~area?
iii
siich a
How rat] tiie security goals be irifluetired to stabjlize tlie dyriati~ics?'" Limit Conditions and optimization of arms race stability
The arrns race stability it~dexcan be spijt irlto two tertns a = aS . rm,rviiere Y. ,
r*
-
$11
'
s.22
$12
'
.$21
,
=
cos
- cos
ros
'1-0s @ 2 1
'
~I~peurEs o~ily011 tlie niar~itialstaciirib e f f ~ c t I>iit s riot oii t tie rtiarsinal c-rists. i ~ l i j k tlie fractioi~a@ cIepeiirIs oii four aiigles. SVi t Ei cPi = @;; - (Dj; tlie iiilmlier of frrp iuigles cari I ~ P furttler redilcecl freiii four to tivo acrording to
'7r
@
0.. E
''
For
cos CP;; = cos
aji
1
+ S ~ I QI i tat1 Q r i
cos O i
'
fixed. oiily cirpr~irlsoii @ i i wliicli act as cun trol aiiglrs For stppi.iiig t lip B ~ S ~ C I I I dynamics givcii Iiy tlie clirectiot~of Tlie coriditiori a = 1 defiiiec a Louxidary betweeti stabiijty atid iustability iri tlie @22)-space.rorresporidirig to a surface iri the four-rfiiiiensioiial space oF variables. For rPii clioseii by side i tile otlier side j can Qi
AZ.
"See the contribution by M . Jathe in this book and [Schef92aj. "0ther forrns of staliilization. as tbe darnpeiiing npar tlie cost thresholrls or other infl iipnces I]: on sectirity, are not considered bete. 12~utuab security cotild Lir achipved if the security-rast effects SC,, > 0 for all actors are positive.
>
I to mairitairi arms rare clioose its cotitrol aiiglc G„ rvitliin tlie lirtlits given liy stability. Tlius, to eiisure stability, bot11 sfrles are forced to coaperate to soIrre rlegree.
It is an irriportarit question whether bot11 sides, tryi~igto tliaxi~~iize their sec.urity ciiaziges AS; i ~ ai cost-effective way for giveii costs (C;;, Cr2) would uriderriliiie arms race stability. Ir] h e r words: is the optiniizatiori oF the uriilateral secvrity Ilieacure ui = s q i / s c i j conipatible with tbe optiinizatiori of t h e iilutual stability measure. g l ; = SC;;/scji'?Tlie dileinma of tlle security-stability iiiteractiori is tliat the maxjmurii for ui is not ri~cessarilytlie saIiie as t h e ~liaxiniumfor r j i , although tlie product of both tias t ticl Same value a = alu2= a l p z r . Tbus, there cali be a coriffict betweeii the optirriizatioti of security gairis atid ttie optimization of arrns race stability (see tIie foilowing sectiori).
Applicat ions
4
Applicatioris of tlie SCX model iriclucle:
TIie iiiterplay lietween the buildup alid reductioti of strategic iiuc.lear wralioIis. defense systems arid counternieasures; tlie iriteractiori betwtteri proliferatioii, niissile deferises arid inter~iationalcotitrols of armamen t and technology; i
tlie inipact of dianges
the worlrl errergy systerti on eiconoriiy, enviroriiiieiit aiid coriflicts (iri particular, the greenliouse problern) iti
While t11e Erst applicatioti lins b e ~ uexariiiried in detail, with soiiie of tlie resillts giveii in t lie followirig, tlie last two are tiew applicatioris which are curreiitly I~piiig studied arid raii tlier~forrbe describcld only as r o ~ i c ~ p t s .
4.1
Strategie Defense and t h e Nuclear Arms Race
The SCX iiioclel lim lie~iiappIied origirially t o tlie strategic artiis rac.e between tlie tivo fornier superpowerso c1esc.ribiiig tlw buildiip üticl reductioii (rlisariiiar~~ciit) tif iiuelear weaporis aiid strategic defense systet~is.A stratesic security fi~iictioriwas iised as a drivirlg force whicli is based on a siiiiple tiva-strike sceliario of iiilclear war, iiicludi~ig forces, first arid secotitl offerisi ve, defeiisive, anc2 atiti-defe~isive(cleferise-suppressio~~ stri ke capabili ties as security c.riteria aiid a riuni ber of parat~ietersli ke niissfle acciirac.y, costs of weapoa systems or the: perceived probability of preeniptioii. For a baseliiie paratneter set a r ~ dselected parailieter comliiiatiolis t h e dytiati~ic.behavior was sirnulated: folcusirig ori trasisi tio~isto uns table or cliaotic behavior. Wi tliiri tlie frar-riework of t lie S CX iiiodel goals for disarnia~iie~it could be forrnulated arid stable patlis Iie seardied for, lookirig far a reductio~iiii the 11iiIitary exprridi t~iresin combination ivit h mutual srtcuri ty aiid stability.
Modelliri p Irtternarional Sccurim Problems in rhe Framewnrk of the SCX Model
Tlie followitig basic variables liave beeii IJSPCI ( 2 , J = 1,2):
in t l ~ eS(."C fratiiework for eacli of tlic
two actors
1. Tlie relevant system variables ,Yki ( X : = 1, ..., 7 1 ) are the offense rapability U; (number of deployed iiuclear warbeacls), the defcirise capabili ty D; (iiur~itrierof irztercepted warheads), a ~ i dt Iie aiit i-tlefezise (deferise siipprcssiot i ) c-alialiitity .4; (reduction iii the defense Dj due to coiiritermeasures).
+
2. TIie costs Ci = C r CF (strategic liudget) represerit t b e aiiriual arri~atrietit expericlitures oC govertinien ts to achieve t heir strat egic goals. beirig tlle suiii of tlie variable. rosis C!: = OXki of chaiigrs i r i tlie riiilitary capaliilities (investnient for procurenierit aiid rleploy~~ierit), a ~ i dthe fixed costs for riiaiiitaitiI X k i ,:C ing tlie tnilitary capabilities (aperatioii aiid iriai~itciiaiice)C:'. = CLl cki are tlie iiiargiiial variable costs per uiiit of AXki,c i i tlie iriargiiial fixed rosts pcr uni t of .Yki.
Er=,
- -
3 . The state depeud~ntsrruritg fzi~ictionnl;'i(S1, ,Y2) is a iitility iiieasure for tlie expec.ted payoff (gaiiis t~iiriuslosses) of Riffereiit aptioiis, iri particiilar. uf stsi kiiig first atid secoiid, depeiidiiig oii tlie state vrctors .?; o i eacli side.
As the security fuiictioii Si a garne-tlieoretic. cor-riliriatiori of different sec.urity r.riteria is i~sed,i iicludirig, i ~ partirular, i t tie relative daniages rreated by firs t arid ser.orid strike:
0: alid 0: a r t~l i ~e f f ~ r t i v(psiietratiiig) ~ offeiisiv~rapal>ilities jwarliea
