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200322:100026788(2003)0220024206,(,400044):L,L:1.;2.,;3.,L,LL:;;;;:F224:ATheGameAnalysisfortheConflictedDevelopingCountriesandtheDevelopedCountriesZHANGRong,LIUXing(CollegeofBusinessAdministration,ChongqingUniversity,Chongqing,400044,China)Abstract:Thetheoryofdifferentialgamesisusedtostudythepossibleequilibriumstrategiesforthetwokindsofconflictedcountries,thedevelopingcountriesandthedevelopedcountries.Firstthedy2namicalgamemodeliscreatedforthem.Thentheoptimalsolutionofthemodelisgivenbythetheoryofdifferentialgames.Equilibriumsolutionshowsthat:1.Iftherestillexistconflicts,theintentionalde2stroyingofthedevelopedcountriesistheiroptimalstrategyatsomespecialphases;2.ThestrategiesfordifferentstagesmaybeverydifferentandthestrategyaRolandforanOliverisnotalwaysanoptimalstrategy;3.Toavoidhugedamageduringthegameperiod,itisalmostinvalidforthedevelopingcoun2triestopursuemeansofeconomyormilitary.Theyshouldfindwaysotherthaneconomyormilitary,suchaspoliticaltalks.Methodsusedinthispaperareapplicableformoregeneralgameproblems.Keywords:differentialgame;conflict;developingcountry;developedcountry;economicgrowth:2001209221:(79970073);(10644):(1969-),,,,,,1,L,[1,2]L,,,,,,;,,,,,,L,?©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,,L,L[3],L,L,,,,,[4],,L,,,,,L,,,,,L:;;;L2,L1)xa1=m1x1-c1vx2xa2=m2x2-c2ux12)J(u,v)=T0[(1-v)x2-(1-u)x1]dt3):x1(0)=x10,x2(0)=x20,0x10x20;4):x1(t)0,x2(t)0;0Fu,vF1;5):c1c2mm1m2;m1öc1Fm2öc2Z,,Zx1x2Z,u,J(u,v);v,J(u,v)Z,,,m1m2,,[5]Z,,,,-c1vx2-c2ux1Z,(1-v)x2(1-u)x1,Z,,,,J(u,v),uq,J(u,v),vl,J(u,v),J(uq,v)FJ(uq,vl)FJ(u,vl)Zu,v.,u,v1,,Z,0Fu,vF1Zx10x20,,Zx1(t)0,x2(t)0,,u=0,v=0522©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved..xa1=m1x1,xa2=m2x2,,x1(t)=em1tx10,x2(t)=em2tx20.0x10x20,x1(t)0,x2(t)0Zu0,v0,xa1=m1x1-c1vx20,xa2=m2x2-c2ux10,,x10x20,Z,,(),,;,x1=0x2=0,x1(t)0,x2(t)0Zm1m2,,,,Zc1,c2GDP()Z,c1c2,Z,c1,c2m1,m2,700,Zm1öc1Fm2öc2,,c1c2mm1m2,,,Z3LHamiltonH=K1(m1x1-c1vx2)+K2(m2x2-c2ux1)-[(1-v)x2-(1-u)x1]HamiltonKa1=-5H5x1=-m1K1+(1+c2K2)u-1Ka2=-5H5x2=-m2K2+(-1+c1K1)v+1,:K1(T)=0K2(T)=0s1=1+c2K2,s2=-1+c1K1,H=-s1ux1-s2vx2+x1(t)0,x2(t)0,u,vu=0,s101,s10v=1,s200,s20,xi=xi(S),si=si(S),Ki=Ki(S),i=1,2,,S=0(S=T-t)s1=10,s2=-10,,u=0v=0,Ka1=-m1K1-1Ka2=-m2K2+1Ka1=m1K1+1Ka2=m2K2-16220032©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.K1(0)=0K2(0)=0K1=1m1(em1S-1)K2=1m2(-em2S+1)s1(t)=1+c2K2=1+c2m2(-em2S+1)s2(t)=-1+c1K1=-1+c1m1(em1S-1),s1(0)=1,s1(S)=-c2em2S0,S10,SS1,s1(S)0;s2(0)=-1,s2(S)=c1em1S0,S20,SS2,s2(S)0ZS1=1m2ln1+m2c2S2=1m1ln1+m1c1m1m2m1öc1Fm2öc2,S2S1ZS0=min{S1,S2}=S2,S0,u=0v=1Ka1=-m1K1-1Ka2=c1K1-m2K2Ka1=m1K1+1Ka2=-c1K1+m2K2K1(0)=1m1(em1S0-1)K2(0)=1m2(-em2S0+1)K1(0)=1m1(em1S0-1)=1m1(em1(1öm1)ln(1+(m1öc1))-1)=1c1,Ka1=m1K1+1,K1(S)=1c1em1S+1m1(em1S-1),Ka2=-c1K1+m2K2K2(S)=em2SK2(0)+em2SS0e-m2s(-c1K1(s))ds=em2SK2(0)+em2SS0e-m2s(-em1s-c1m1(em1s-1))ds=1m2(-em2m1ln1+m1c1+1)-1m1-m2(em1S-em2S)-c1m1(m1-m2)(em1S-em2S)-c1m1m2(1-em2S),S0,s2(S)=-1+c1K1=-1+em1S+c1m1(em1S-1)0,,v=1Z722©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.s1(S)=1+c2m2(1-em2m1ln1+m1c1)-c1c2m1m2(1-em2S)-c1c2m1(m1-m2)(em1S-em2S)-c2m1-m2(em1S-em2S)Zs1(S),s1(0)=1+c2m2(1-em2m1ln1+m1c1)1+c2m2(1-em2c1)Z1+c2m2(1-em2c1)0,m2c1ln1+m2c2Zln1+m2c2m2c2-m222c22,m2c2-m222c22m2c1Z(2-m2)c12c2Z,,Zs1(0)=1+c2m2(1-em2m1ln1+m1c1)0Zs1(S)=-c1c2m1m2-c1c2m1(m1-m2)1m1em1S-1m2em2S+c1c2m2(m1-m2)em2SS0Z,S1,0SS1,s1(S)0,s1(S)0SS1,SS1,s1(S)0,s1(S)SS1,S,s1(S)0,s1(0)0,S2S1,SS2,s1(S)0,0SS2,s1(S),s1(S)0ZS2,SS2,u=1v=1Ka1=-m1K1+c2K2Ka2=c1K1-m2K2Ka1=m1K1-c2K2Ka2=m2K2-c1K1K1(0)K2(0)S2,K1(S2)K2(S2),,S2K1(S)K2(S),s1(S)s2(S),,Z4,Z1.ZT-S0-S2,u=1,v=1,Z:u=0,v=1,,Z,J(u,v)=T-S0-S20[(1-v)x2-(1-v)x1]dt=J(u,v)=T-S0-S20[-x1]dtZJ(u,v),;,,xa1=m1x1-c1vx20,,Z,v=1Z,,,v=1Z,J(u,v),;,,Z,Z,,Z,u=1,v=0,Z8220032©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2.[T-S0-S2,T-S0],u=0,v=1,,,;,Zu=1,v=1ZZ,Z,,,Z,;,,,,ZZ,,,Z,,,,,Z3.[T-S0,T],u=0,v=0,,,u=1,v=1ZZ,,u=1,,,Z,Z,v=1,Z,,,Z4.,,[0,T-S0]Z[T-S0,T],S0=1m1ln1+m1c1,c1mm1,S01c1,c1,,m1c2,ZZ,Z,,Z,?,Z,,Z5.Z,[T-S0,T],[0,T-S0],S0Z,TZ,T,Z,,T,ZT?T,T,Z,,,,,Z6.ZS2,S2ZS2s1(S)=0,s1(S)=0S2,s1(S)=0(85)922©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.[7].[J].,1994,10(3):327-332.[8],.[M].:,1990.[9],.[M].:,1990.[10].[M].:,1993.[11],.[J].,1993,29:26-33.[12]ZhengZhongguo,Virtualsystemmethodforsystemtree[J].ChineseAnnalsofMathematics,1995,16(4):509-518.(29)S2=1m1-m2ln(m1öm2)(m1-m2)+m1+m21m1,m1m2,S2Z,T-S2,Z,Z,,S2,T-S2,Z,,,,,,,ZZ5,LL,L:1);2),L,L3),,,L:[1]JackHirshleifer.Appeasement:Canitwork?[J]AmericanEconomicReviewPapersandProceedings,2001,91(2):342-346.[2]StergiosSkaperdas,ConstantinosSyropoulos.Guns,butter,andopenness:ontherelationshipbetweensecurityandtrade[J].AmericanEconomicReviewPapersandProceedings,2001,91(2):353-357.[3].[J].,2001,(4):5-8.[4].[M].:,1987.[5]Jones,CharlesIrving.IntroductiontoEconomicGrowth[M].NewYork:W.W.Norton,1998.582MTBF©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.