Effects_of_War

An Analytical Model for Conflict Dynamics Author(s): N. Gass Reviewed work(s): Source: The Journal of the Operational Research Society, Vol. 48, No. 10 (Oct., 1997), pp. 978987 Published by: Palgrave Macmillan Journals on behalf of the Operational Research Society Stable URL: http://www.jstor.org/stable/3010117 . Accessed: 24/09/2012 08:59 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . Palgrave Macmillan Journals and Operational Research Society are collaborating with JSTOR to digitize, preserve and extend access to The Journal of the Operational Research Society. http://www.jstor.org journal of the Operational Research Society (1997) 48, 978-987 ' 1997 Operational Research Society Ltd All rights reserved 0160-5682/97 $12.00 An analyticalmodel for conflict dynamics N Gass Decision Matrix, Ottawa, Canada A coherent dynamic conflict model is developed from basic principles. The governing equations have a striking resemblanceto the continuity equation in fluid dynamics with an additionaltern for the response to pressureby the opponent. The salient feature of the model is a moving confrontationline which is an excellent indicator for the evolution of conflict. The developed model also permitsinvestigationof the necessaryminimuminvolvementof a third organizationto establisha statusquo between the actors.The model is demonstrated partyactorsuch as an international on the Russian-Chechenconflict and the Bosnian war. Keywords: conflict analysis; methodology; modelling Introduction With the new political world order, a new distribution of power has risen in the form of a multipolar system where the manifold of interactions of political, social, economics, and military environments tends to raise the ambient level of regional conflicts potentials. This will inevitably have an impact on the international crisis management, policy planning and the structures of peacekeeping forces due to the widening theatre of operations and the new modes in which they are conducted as discussed by Bailey and Ferguson.' But most important, early recognition of potential conflicts will open additional avenues for conflict resolutions as analyzed by Kaufmann2 and Bennett3 and thus will have a higher chance of success to stabilize volatile geopolitical regions. Richardson4 started the trend of mathematical modelling of conflicts well before the Second World War and since, numerous models based on a wide variety of mathematical approaches have been developed as, for example discussed by Nicholson,5 Gillespie and Zinnes,6 Fraser and Hipel,7 and Gass.8'9 In the development of conflict models, two major problems have to be overcome. The first is the choice of the governing equations which are often selected from other disciplines and adapted to suit the present application without regard to the mathematical structure and whether it reflects the basic laws of the processes to be modelled. The other problem is the choice of conflict parameters and their numerical values. Clearly, the relationships between actors are very complex and many rational and subjective considerations influence their behaviour as described by Nicholson. 10 Correspondence: Dr N Gass, Decision Ottawa, Canada, KIS OA4. Matrix, 77 Havelock Street, The present paper is an attempt to eliminate the first problem by developing a coherent set of differential equations based on basic principles in conflict theory. The second problem is also addressed through the choice of some global parameterswhich are easier to estimate. Nevertheless, the underlying numerous subjective factors, such as ethnic particularities, world opinion, inherent animosity, etc., which are often the impetus for irrationalactions, are difficult to describe in a rational way. The final results of this approachis a moving confrontation line which indicates an imbalance in the status quo between the actors. This imbalance can be used, for organizationas an early warning example, by international signal of possible conflict escalation. It must be pointed out that the proposed model does not predict future conflicts at a precise time but rather investigates the conditions which may lead to such events, in a similar way to the approachesby Nicholson,5 Gillespie and Zinnes6 where conditions of stability and equilibrium are studied. Also, the hypothetical question can be studied of how much intervention by an international organizationis necessary to balance the pressure at the confrontationline and thus stop its movements. The governing equations are solved by using the commercially available software tool ithink, produced by High Performance System Inc., Hanover, NH, USA. ithink is a dynamic systems tool ideally suited for trackingtime-dependentevents. Another advantageis that the results are automatically displayed in graphical form at each time step. With this feature, an analyst may interfere in the computation process at any given time to update or alter various conflict parametersin order to study some 'what if ..' questions. A complimentarycopy of the programmedconflict model is available from the author. NGass-An analytical for model conflict 979 dynamics Finally, it is worth mentioning that the governing equations are also applicable to analyze conflicts arising in labour relations and contractnegotiations. Basic assumptions Conflict situations can be caused by many factors such as differences in political ideologies, legal and economic systems, ethnic and social particularities, human rights issues, state-sponsored terrorism,cross-border environmental problems, territorialand resource claims, etc. Many of these issues may be subduedfor some time until propelled forward to surface at the confrontationline between the actors giving rise to pressure. A detailed list of factors is given by Gass.8 Consider the different conflict elements between actors A and B depictedin Figure 1. Let the individualissues have virtual distances from the confrontationline and different speeds at which they move towardsit, namely towardsthe negotiationtable, UN or WTO forums, or towardsmilitary action,etc.Atthe confrontation theseissueswill be metby line, moreorless resistance fromthe otheractorandwill causepressure. Let an international organizationinfluence the actors to decreasetheirconfrontation using, for example,political by pressure,economic force, or peacekeepingoperations. Let the perceived important the issues S4 and SB of the of actorsA and B be multipliedby the capabilitiesCAand CB (political power, economic strength,military force) to lend weight to their issues. For example, if an issue raises a large confrontationbetween a superpowerand a weak opponent, the formerdoes not need to worrymuch while the latterhas to fear possible military actions. Conversely,if there is no then a militaryimbalanceis of no importance confrontation, for as is the case betweenFranceand Luxembourg, example. With these assumptions,two generalizedforce density or pressurefunctionspA(r'A,t') and pB(r/B, t') for actors A and B, respectively,can be defined as pA = iA N A/ and NB pB=E cisi(i 1 -d EB (r/B-ri), CB for all O H) = 0 where H denotes the width of a more qp(Ir or less narrow virtual area along F (see Figure 1). H can be viewed as the issue horizon where within this virtual area, all issues are of concern at present, while outside, they are more or less subdued until moving forward into the confrontation zone F ' H. Clearly, an actor must choose the span of H such as to include all issues of concern. Finally, let the concentration of issues ,u be given by the integral over all issues inside the confrontation zone F ' H Table 2 (9) With this, equations 7 becomes pA +'pAdiv pB +'pBdiv B UA+ RB = ' = UB +RA o ( These equations are integrated in Appendix A Dynamic confrontation line Further analytical treatment of the conflict equations A7 and A8, developed in Appendix A, is possible by choosing the distributions 9A = (A(F - rB) and 9B = 9B(rA - F) of the response effectiveness over the depth of the issue horizon H. Let these functions have the simplest form possible with the conditions at the confrontation line 9(A(O) = 9B(O) = 1 and at the horizon sA(H) = YB(H) = 0 which is satisfied by a straight line. Thus, A (1/HB)(F - rB) + 1 and 9B = (1/HA)(rA - F) + 1 and 9pB = 1/HA. Let zA= -0, with 9IA = 1/HB = i-B, and v7 = -F be the velocities of the issues and vB the confrontation line, respectively and letpA(t) = CASA(t), etc., by definition, where CA and Ce are assumed to be constant over the issue horizon. With this, and setting SA(t) SB(t) SB (H) SA(H) Chechen response profile Russianpressure pB 0 Capability of imbalance CA-CB A 0 0 0 B 0 A B C B B C D C C D E D D E F E E F -F -E -D 0 0 0 -C -B -A 0 0 0 0 G A A B B B B C C C C D D D D E E E E F F F F F F of Research Vol. No.10 Society 48, 982 JournaltheOperational equations A7 and A8 become oA(vF - A) + WA + RB = WB-RA = 0 ( where u = v4/vB. For numerical purposes, it is of advantage to transformequation 16 in a nondimensionalform as = )[ B(+ A ) UB(VB+ 'F)_ VF where WA and We denote the issue withdrawals of actors A and B WA = HA{w WB = HB{WB (1+U [ :( +# R )]17 + (1 -w + )A }( C + 1) 1) 12 (1) *1'u)[l+ ~WA 'RB) (17) (1 - WB)'EBJ(UB and RA and RB are the responses to the other actors issues or demands RA = HB{(CA - = where cx (SA(t)/SB(t))is the issue ratio at the confrontation line and ,B= (SA(H)/SB(H)) is the issue ratio at the horizon. CB) 0 CBSB(t)} X1 - (-)S(){+ (13) Simple examples RB =-1 BHA{(CB _ CA) 0 CASA(t)}(I -' B) B B(H)){2'cB} (A S) S(H) Consider the simple case where vB = WA = WB = 0, and c = ,B.Then equation 17 becomes A = (RA/RA + RB) which X Substituting equations 11 into each other and resolving for vF leads to the equation of a moving confrontation line according to the pressure differential between the actors. Thus, A+ B)v =AvA - BvB - WA + WB + RA - R (14) confirms the obvious situation that the confrontationline moves faster in favour of actor A if there is less resistance RB by actor B or more resistanceby actor A against B. If actor B does not resist the issues of A then A = 1, and the confrontationline moves with the same speed as the issues of A arriveat the front. Figure 2 depicts the relation between the power ratio C/Cl3 and the issue ratio cx.For this, let WA = WB = 0, H/HB 1 'A = gB = 0 = 1, CA = CB = 0. The Cold War scenario can serve as a trivial check of equation 14. Let there be no withdrawal and no interference by an external actor. Let the perceived capabilities and importance of all issues including their speeds and issue horizons be equal. With equations 12 and 13, equation 14 becomes 2cvF = TAH{0 Let the actors be completely rational, such that their reactions depend on the power ratio C4/Ce. Thus, zA/zB ac CA/CB, and (CB-CA) ' pA Oc CB/CA . (CA _CB) ' pB o CA/CB Then equation 17 becomes o [ ' 1qDf]-[1'[ + d= + / (CA/CB)4 (2 + (X)(X2/(l + 2cc). 09 CS(t)}B -_,BH{O 0 CS(t)}A The confrontation line becomes stationary if the aggresstion rates r and the pressure response terms 0 0 CS are equal. During the Cold War period, small perturbations about the equilibrium were present reflecting the different attitudes and viewpoints vis a vis the balance or military power and external political influences. For this, let IA =, TB = oX, R = {O 0 CS(t)}A and {O0 CS(t)}B = fR. Then, vF = (1 /2)TRH(oc - /) where a and 3 are small perturbations about 1 which cause slow oscillations of the confrontation line. The relationships between the speeds of the issues towards the confrontation line can be given as v + vBI, 1 (WA +RB) crA 1(WB+ crB RA) It is interestingto note that, even for low issue ratios cc,a power ratio of more than 3 does not warrantthe additional resources since the speed of the confrontation line is nearing its maximum of 1. For power ratios less than 1, the confrontationline moves against actor A despite high issue ratio. In other words, actors moving forward issues without the backup of power, will not be taken seriously. Figure 3 shows the relation between the speed of the issues moving to the confrontationline and the power ratio. 1.0 x 0.5- a=2 a4-1 0.0- (15) With this, equation 14 becomes -0.5 - 0 1 2 C 3 F I aB (1 + UW +.B R )-CA (1 + )(Yx + RB() CB Figure 2 Influenceof issue density ratio cx. NGass-An analytical for model conflict dynamics 983 1.0 0.5 I----- The Chechen-Russian conflict -05 O 1 2 CA C B 3 Figure 3 Influence of issue speed ratio u. With above numerical values and o = 1, equation 17 becomes B 4- 1 CA 41-i 1'u[ (cA 1+u [ \CB,/j The influence of the issue speed ratio u is most pronounced between 2 < CA/GB < 3 which is in the region of transition in the dominance of power between the actors. For a power ratio greater than 2, u has practically no influence on A and there is no need to increase resources. In comparison to Figure 2, Figure 4 depicts an actor who is submissive if the power ratio is balanced as shown in Table 1 and even more so if CA/CB < 1. The resistance term RA becomes negative which indicates cooperation and results in a high speed (less than - 1) of the confrontation line against actor A. For power ratios greater than 1, actor A becomes increasingly aggressive similar to Table 2. The graph also shows that the decision of actor A occurs in leaps and bounds according to some thresholds whereas in Figure 2 an infinitesimal action by actor B caused an infinitesimal reaction by actor A. Russia regards the Caucasus as a vulnerable flank vis-a-vis the neighbouring countries Turkey, Iran, and the general influx of revolutionary ideas from Islamic countries give Russia ample reasons for 'protecting' the region. Equally important are the economic reasons since the region is rich on mineral resources and oil. Some of the current instability of the Caucasus originates from the Russian colonial expansion and the long Caucasian War in the last century. Others stem from the Stalinist method of splitting ethnic groups through artificial division of regions into administrative entities. For some years, Russia has tolerated the secessionist government of Chechnya but in 1993 has begun to take military steps to resolve the impasse. The reasons for the resistance to Chechnya's independence is Russia's determination not to relinquish control of the region since there are fears of a domino effect if Chechnya separates. These fears are justified because there are several other candidates for separation in the Caucasus, notably, the Tartars, Karachai, Lezgins, and Ossetians, to name a few. Chechens have a long reputation for opposing the Russians, as was the case in the Caucasian War, despite having a much inferior military force. Such attitudes are reflected in the term (CA - CB) 0pB which can be eval- 1X0 .0 3 -2.0 02 1 2 0A Figure 4 Influence of issue density ratio a for a submissive or actor. agressive uated by developing the response matrices given in Tables 2 and 3. The advantage of such an approach lies in the flexibility in describing the influences of numerous rational and subjective criteria on the response of an actor. Indeed, it would be very difficult to develop functional relationships for this purpose. For clarity reasons, the rating scale for the capabilities and resulting response is chosen as {0, A, B, . . ., F) where A denotes a low level of issues arising, weak capability, or little response, while F represents the opposite. The choice is arbitrary but it is ideal to demonstrate the combinatorial rules of the algebra 0. In the associated computer program, however, these alpha-numeric ratings are converted to an arbitrary numerical scale, as for example A = 1, ..., F = 6. The response term shows that Chechnya, denoted by the superscript A, is not submissive or ready for concessions even when faced with an overwhelming military imbalance CA - CB to Russian's advantage paired with high Russian pressure. For example, if the capability imbalance is - E (large), and Russia's pressure is E (high), the response (CA _ CB) &pB = D (mediumhigh) at which Chechnyais resisting Russian demands or issues. Initially, from 1991 to 1995, Russia sought to resolve the issues with Chechyna through political and economic threats and later through some military actions. Chechnya is politically important to Russia and this is why the Russian response to the Chechen issues is aggressive as seen in Table 3. 984 JournaltheOperational of Research Vol. No.10 Society 48, Table 3 Russian response profile for 1991-1995 Chechenpressure pA 0 Capability imbalances CA - A 0 0 0 B 0 0 0 C A A B D B B C E C C D F D CB 0 A B 0 0 0 C D E F O O 0 0 A B B C C D 0 0 A B B C C D D E D E E F D E E F F F Since there is no external intervention WA and equation 17 becomes VF I_ I_ - WB = 0, t+ VB (+ D ( + P(ucxp - (18) where p = RA/RB.In 1990-91, Russia was preoccupiedby othermattersand paid little attentionto the issues concerning Chechnya. Thus, vB = 0, and TB = 0 yielding RB 0 and A becomes A = (p/I + p) = (1 + (RB(t)/RA4(t))j1 = 1. First reactions by Russia occurredafter PresidentDudajew (in October 1991) unilaterallydeclared independence and, in retaliation,Russia declareda state of emergency on Chechnya, threateningpossible military action. The parameters were assumed as: a = ,B= 1, HA = HB = 1, SA(H)/SB(H) = 1, SA(t)/SB(H) = 2, SB(t)/SA(H) = 1, 2, v = 1, SA(t)/SB(H) = 3, SA(t)/SB(t) = 3, CB/CA = B (CB CA) 'pA C = B = 2, (CA-CB) pB = B0 C = C = 3, and vB = 0 since Russia applied only passive resistance. With this, the response terms becomes - In September 1994, President Dudajew declared a state of war and in November 1994 the opposition started an attack on Grosny. In January 1995, Russian troops moved towards Grosny and in February 1995 the capital fell and fighting spread to other areas. During this period the threat parameters were steadily approaching the values of TA = = 3, TB = 1, with u = 1, SA(t)/SB(t) =-, CB/CI = C Q D = C = 3, CA) 'pA (CA-CB) pB= (CB ' C = C = 3, and equation 18 becomes C A= 2 with P = 3 (_B(t))_ RA(t) = 15 TA(t) and A = (I + (8z (t)/5zA(t))) TB RB(t) = 6TB(t) which yields The threat parameters were initially TA = 0.5 and = 0.2 but steadily increasing until in August 1994 a coup was launched by the opposition, also supportedby Russia. This caused a slowdown of the advance of the conformationline as depicted in Figure 5 with the threat parameters reaching now TA - TB - 0.6. 0.0 0 eaA Xo (=,; C) D ;s\s. ;;s .-.. .. . . ......... g . optimistic view . ' ........................ ....... . -., . L Figure 5 shows that the conformation line moves now against Chechnya, an indication that Russia is controlling the conflict. Recent Russian elections, economic considerations including military resources, and negative public opinion forced Russia to reduce the crisis which could lead to a new, more relaxed response matrix given in Table 4, a pre-requisite for negotiations. In September 1996, a cease fire was announced but a solution of the conflicting issues has yet to be addressed. Russia is reluctant to permit Chechnya to become an independent country and thus Chechnya may raise the issue pressure which could result in unrest over the next few years as shown in Figure 5. Using Tables ' =-0 ' A = B = 2 and 2 and 4 yield (CA-CB) pB (CB C) 0 pA = O 0 D = A = 1 and assuming an optimistic and pessimistic threat parameter such that p (optimistic) =2 and p(pessimistic) = 9 leads to a slowly increasing speed of the confrontation line driven by unsettled issues. The Russian response given in Table 4 and a moderate threat parameter prevents a negative A namely, a Russian advance but encourages Chechnya to pursue the goal of independence. ; f . . .. External pressure 1991 1996 2000 year Figure 5 Russia-Chechnyaconflict. External pressure can decrease the imbalance between the actors A and B expressed by the movement of the confrontation line. An improvement special case is the status quo 985 dynamics model conflict analytical for NGass-An Table 4 Russian response profile for 1996-2000 Chechen pressure pA 0 Capability imbalance CA-CB 0 A B A 0 0 0 B 0 0 0 C 0 0 0 D A A B E B B C F B C C 0 0 0 C D E F O O 9 0 0 0 0 0 0 0 0 G A A B B B B C C C C D D D D E E where vF = 0. The necessary minimum interventions'X(t) and gB(t) can be estimatedby using equation 16 to yield u(WB' RA)- a (WA +RB) (19) Ignoringthe 'voluntary'withdrawalratesw, above equation becomes 'B[B Figure 6 depicts the speed of the confrontation line against external interventions for some power ratios. Actor E acts only on actor A and it can be seen that, for power ratios CA/CB > 2, it becomes increasingly more difficult for actor E to make an impact on A. For high powerratios,the involvementratioEA/CA must move closer to 1 before A changes significantly. The Bosnian conflict + uuA(AB+1)] - [A'A+ H (A + 1)] +A-B=O (20) where A= 1 U and B = !TBUBH 1~~~~~~~~ CA{ (CA _ CB) & pB } (2 + CA) (21) _ B(CB CA) CpA(t)}( P) 1(2 + CB). (23) There are many combinationsof eA and BB which render vF = 0. However,the most desired solution is not only the minimum efforts EAICA and EB/CB but also considers the 'political correct'solution including factors such as legitiproblems,social condimacy of issues raised,humanitarian tions, etc. Thus, an external actor has to select the most combinationsamong the set of possible soluappropriate tions. All parametersin above equations are time dependent and, in orderto keep vf = 0 over a longer time period, the efforts EA and EB have to be readjustedconstantlyto offset changes in the conflict evolution. In the special case where an external actor fully suppresses the reaction RA or RB of actors A and B by BA = gB = The decades old subliminal ethnic conflicts in the socialist Yugoslavia surfaced after Solvenia and Croatia declared independence in 1991. In Spring 1992 fighting started in Bosnia-Herzegovina with the declaration of a Serbian Republic of Bosnia. The United Nations (UN) placed an economic embargo on Serbiain May 1992 with additionalsanctionsintroduced in May 1993. Nevertheless, one year later,the Bosnian Serb forces had capturedmore than two-thirdsof the territoryof Bosnia-Herzegovina. The confrontation front against the Bosnian Muslims moved very swiftly as shown in Figure 7. The UN peacekeeping forces stationed in Bosnia since aid. 1992 were increasinglyunable to provide humanitarian by the UN not to use force was taken by the The restraint Serbs as a sign of weakness which hamperedUN activities and also had a negative influenceon the peace negotiations. Towards the end of 1995 the UN finally did use air strikes to enforce a safety zone around Sarajevo. For the simulation, the following numerical values were selected with the indices A and B denoting the Bosnian Moslem O.75 e cZ ='= ---~.............. ' ............ terms uuA In anotherspecial case (as, for example, in the Bosnian conflict) where an external actor pressuresonly one of the actors, equation 21 becomes eB = B - A/2 + B where = CB = 1 with the admissible solution CA = O, and u = CA 0 __0A3 CA=4 CA=1 CA =1/2 -0.75- CA =2 0 1 2 3 EA 4 Figure 6 Influence of external intervention. Society 48, Research Vol. No.10 of 986 JournaltheOperational 1.0 .poptimistic view 2 -0-02 a)~ ~ ~~~~~~ya coue7TeBsna -1 0 . .... .. ofit *.... 1991 forces and the Bosnian 1996 Serbian forces, ...... r.. year 2000 esspecticviewyc=2 conflict. Figure 7 The Bosnian forces and the Bosnian Serbianforces, respectively:a HB /C= CB =2, H4 /31, u = I CA1 4, o=1, zA = l and CB) QpB (CA = O, z= = 2, 3, =1, (CB - CA) 'pA = 5. The military force applied by the United Nations (UN) in a small but highly sophisticated operation matched completely the Bosnian Serb forces, thus which gB = 1. Using equations 12, 13, and 17 yields A = indicates that the issues of the Bosnian Serbs lost pressure and the confrontation line retreated as depicted in Figure 7. These events marked the turnaround in negotiations and in Spring 1996, a peace treaty between the actors had been negotiated (the Dayton accord). To bring both actors at the negotiation table, and to reach a status quo at A = 0, the UN had to apply the minimum pressures of u4 = 4 and eB = 2. This result was calculated by 1, and with u = cA = c= using equations 20-22 _ cB) ' pB = (CB _ CA) '$ pA = 2. (CA The reached peace treaty is far from ideal but the two actors are economically ruined and this is part of the reason why the aggression coefficient T may be small for the moment and thus reducing the chance of a renewed conflict considerably. To estimate a possible confrontation in future, a hypothetical case is studied where it is assumed that the UN would withdraw but its accumulated impact over the past years would not evaporate completely. Let the two actors more or less restrain themselves about the equilibrium conditions 1 but increasing slowly u = a = p = u, with initially I, over time in favour of the stronger Bosnian Serbs. The movement of the confrontation line is then given by A = (1 - p2)(1 + [L)-2 which is depicted in Figure 7 from 1996-2000. The lower bound is the more pessimistic case where the actors begin to be dissatisfied with some terms of the peace treaty while the upper bound denotes with more or less satisfaction. From this, it can be concluded that no serious conflict will arise in the next few years. 4 of conflict. Clearly, the higher the speed, the more imbalance exists between the actors and the more likelihood there is for the outbreak of war. It was found, that the analysis of conflict should be done in two parts. The first part simulates past events in order to establish benchmark values for the numerousparametersin the equations. In a second part,these parametersthen can be varied to study a number of hypothetical future events in the realm of the what if.. environmentto obtain optimistic or pressimistic views. In this way, a catalogue could be created, based on historical event, to associate the speed of the confrontation line with the actual magnitude of a conflict. Thus, the gravity of a futurescenario can be analyzed from the speed of the confrontationline as the events evolve. Also, the hypothetical question can be studied of how much invervention by an international organization is necessary to establish the status quo between the actors. This study will open additionalavenues for conflict resolutions and thus will have a higher chance of success to stabilize volatile geopolitical regions. Appendix A Integration of the conflict equations To facilitatethe task of integrationof equations 10, let F be only time dependent.Then the withdrawalof some of the issues of actor A from the confrontation line can be by: approximated pAdiv UA =pAWA(t) + PA(I -W (t))'A (Al) where 0