ֻ29जֻ11௹(ሹֻ215௹) 系 统 工 程,୍11ᄅ````````````SystemsEngineeringNov.,2011໓ᅣщݼ:1001-4098(2011)11-0115-04ջൈᇌ֥؟ܪܞ୶ଆࠣః໗קྟX姚洪兴1,张 芳2(1.ࡾ්ն࿐ҍࣜ࿐ჽ,ࡾ්ᆓࡾ`212013;2.ࡾ්ն࿐࿐ჽ,ࡾ්ᆓࡾ`212013)ᅋ`ေ:研究了调整函数中引入时滞的有限理性多寡头古诺竞争模型,分别建立了成本函数为线性形式的双寡头及通信市场中成本函数为线性形式的三寡头竞争模型。分析了双寡头模型中的纳什均衡点及通信市场三寡头模型市场行为。时滞的引入更加有效地延迟了市场混沌分岔等行为,当某些参数发生变化时,影响系统的稳定性,并数值仿真分析了系统稳定性。ܱՍ:有限理性;寡头竞争;时滞;混沌;纳什均衡ᇏٳোݼ:F223```໓ངѓ്:A``ܪ൧ӆႮഒඔࠫࡅӌഅ॥ᇅ,ᆃུӌഅࣜႏཌྷࠇཋྟטᆜӌഅ֥චܪࣩᆚbֻ2ࢫܼѩࢲކൌ࠽ཌྷර֥Ӂ,ૄ۱ӌഅሔ০ቋն߄bචܪ൧ӆ൞ؓݓ3G๙ྐ൧ӆܪଆቔਔٳ༅bѩࣉྛਔඔᆴ၂ᇕགྷൌᇏ௴ђթᄝ֥ࣜ࠶൧ӆ,ᄝᆃᇕ൧ӆᇏ,ӌഅ҂ٟᆇbֻ3ࢫࢲંbࣇေ۴ऌ൧ӆླaӮЧݦඔߎေ۴ऌؓ൭֥ྛູটࣉྛӁਈथҦbႵሢб؎൧ӆ۷ູگᄖ֥ࣜ࠶ྛູb୍࣍ট1 带时滞双寡头模型建立及分析,၂ུ࿐ᆀؓචܪ൧ӆࣉྛਔ࣮,Bischi֩۳ԛਔႵཋᄝ၂۱ܞ୶චܪࣩᆚᇏ,qi(t)іൕֻi۱ӌഅᄝtྟטᆜ؎൧ӆ֥၂Ϯྙൔ,ѩ࣮ਔᆃᇕหྟ༯༢ൈ௹֥Ӂਈ,i=1,2bp(qi(t)+qj(t)),i,j=1,2,ij֥ಆअၛࠣअ҆໗קྟ[1]bAhmed֩ᄎႨJury่ࡱіൕtൈ௹Ӂླݦඔ,ऎႵೂ༯ྙൔ:࣮ਔႵཋྟטᆜ֥Puuଆ,ѩ࣮ਔऎႵႵࢸྟหp(t)=f(Q)=a-bQ(t)(1)ᆘ֥Нွථଆ[2]bAgiza࣮֩ਔ֒ӮЧݦඔູ٤ཌྟఃᇏ,Q(t)=q1(t)+q2(t)ູሹӁਈ,a,bູ٤ڵ֥ҕඔ,ൈ֥Ⴕཋྟטᆜ֥චܪଆ[3],ѩܼ֞ਔܪଆaіൕ൧ӆഈھӁ֥ቋۚࡎ۬bCi(qi(t))іൕֻi۱ӌ[4]bFangChen,JunHaiMa,XiaoQiangChen࣮֩അ֥ӮЧbପહֻi۱ӌഅ֥০ݦඔູ:ਔݓ3G൧ӆ֥ܪ൧ӆଆ[5]࣮0i(t)=f(Q(t))qi(t)-Ci(qi)(2)ਔᄝቋႪّႋᇏࣩᆚؓ൭֥Ӂਈഈࡆೆൈᇌ,ѩ۳Ⴭಃᇗ``ӌഅiᄝt+1ൈ௹֥০ቋն߄֥Ӂਈ൞ࠎႿؓٳ֥Ⴕཋྟטᆜචܪࣩᆚ,ѩඔᆴٟᆇ֤ԛਔᄝؓ൭j֥ყ௹ّႋҐ౼֥,ӌഅi֥ቋႪّႋູ:ཌྷҕඔ༯,ࡼࠁᚧӾᄝڸ࣍ൈԛགྷ֥ࢲં[6]bqi(t+1)=ri(qej(t+1))܇Ⴅ࣮֩ਔ҂Ѱᒮܒൔ༯֥ܪࣩᆚଆ[7]bਸ਼=argmax[p(qi(t)+eqj(t+1))qi(t)-Ci(qi(t))]ຓ,ᄝః֥၂ུ໓ངᇏ࣮ਔႵཋྟטᆜӌഅҕა(3)ࣩᆚ֥ܪ൧ӆଆ[8-10],൞གྷൌޓ؟౦ঃᇏ൧ӆ൞ऎ``eqj(t+1)ູӌഅiࣩؓᆚؓ൭j֥༯၂֥҄ყ௹ӁႵ࠺ၫྟ֥,ቓԛӁਈטᆜथҦൈॉ੮֞ഈ၂ൈ௹മᇀഈਈbᄝܞ୶ଆᇏeqj(t+1)=qj(t)bഈൈ௹֥Ӂԛູҕॉ൞٤ӈႵсေ֥bࡌഡӌഅູႵཋྟטᆜӌഅ,ૌ۴ऌш࠽০Ч໓ࡹ৫ѩٳ༅၂োᄝטᆜݦඔᇏႄೆൈᇌѩٳ50i(qi(t),qej(t+1))ಃᇗ֥Ⴕཋྟטᆜӌഅҕაࣩᆚ֥ܪଆ,i,j=1,2,ijটטᆜሱ֥࠭Ӂ,۷ູႵ5qi(t)ིӾࠁᚧԛགྷbֻ1ࢫࡹ৫ླݦඔູཌྟ֥ջൈᇌႵX൬۠ರ௹:2011-05-26;ྩרರ௹:2011-08-21ࠎࣁཛଢ:ݓࡅሱಖ॓࿐ࠎࣁሧᇹཛଢ(70871056);ࡾ්സoੂնದҌۚڂpཛଢቔᆀࡥࢺ:ိޠྖ(1964-),ଳ,ࡾ්ྖ߄ದ,ࡾ්ն࿐࢝൱,Ѱൖള֝ഽ,࣮ٚཟ:ሧაڄག;ᅦٙ(1988-),୯,ފଲଲဝದ,ࡾ්ն࿐࣮ള,࣮ٚཟ:ࣜ࠶໗קྟb
116༢``۽`ӱ``````````````````2011୍ਈ,Ⴕೂ༯ྙൔ:E0=(0,0,0,0)50ei(qi(t),qj(t+1))qi(t+1)=qi(t)+Ai(qi(t)),Ea-c1a-c151=(,0,,0)qi(t)2b2b(8)i,j=1,j(4)a-ca-cE22``2=(0,A2,0,b2)bi(qi)ֻູi۱ӌഅ֥טᆜҕඔݦඔbᄝޓ؟໓ᅣ[4-6,8-10]֥࣮ᇏҐ౼ਔAi(qi)=Aiqi(t)ᆃᇕྙൔbE*****=(q1,q2,q1,q2)ॉ੮۴ऌqi(t-1),qi(t-2),l֩ൈ௹֥Ӂਈ,ѩٳఃᇏ*a+c,q1=2-2c1*a+c2c2,q=1-.҂֥ಃᇗ3b23b,ᄵ۷ࡆژކൌ࠽౦ঃbၹՎ,Ч໓֥ႵཋྟEטᆜӌഅ֥ӁਈऎႵೂ༯ྙൔ0,E1,E2ູႵࢸनޙ,֒:2c1-c2<ae(q(9)i(t),q(t+1))qi(t+1)=qi(t)+AD50iji(q),2c52-c1<aqi(t)ൈE*ູNashनޙׄbi,j=1,2,ij(5)ؓႿ༢ᇏ၂ׄ(m1,m2,q1,q2)ԩ֥ॖбइᆔႵ``Dq=
Tqi(t-l)Xl,Xl0,
TXl=1,l=0,1,2,༯ਙྙൔ:i=0l=0l0010,T,XlູಃᇗbT=1,Ci(qi(t))=c0001iqi(t),ci(i=1,2)ູӌഅiֆJ(m໊Ӂ֥ሹэӮЧbսೆ(5)ᇏᄵႵ1,m2,q1,q2)=(10)A10B1C1q0A2B2C21(t+1)=q1(t)+A1[X1q1(t)+(1-X1)q1(t-1)]`````õ(a-c1-2bq1(t)-bq2(t))A1=A1(1-X1)(a-c1-2bq1-bq2)qA2(t+1)=q2(t)+A2[X2q2(t)+(1-X2)q2(t-1)]2=A2(1-X2)(a-c2-2bq2-bq1)`````õ(a-c2-2bq2(t)-bq1(t))B1=1+A1X1(a-c1-bq2)-4bA1X1q1(6)-2bA1(1-X1)m1(t)mB2=1+A2X2(a-c2-bq1)-4bA2X2q2i(t+1)=qi(t)ᄵູೂ༯֥ඹົ༢:m1(t+1)=q1(t)-2bA2(1-X2)m2(t)mC2(t+1)=q2(t)1=-A1b[X1q1+(1-X1)m1(t)]qC1(t+1)=q1(t)+A1[X1q1(t)+(1-X1)m1(t)]2=-A2b[X2q2+(1-X2)m2(t)]`````õ(a-c1-2bq1(t)-bq2(t))``नޙׄԩ֥໗קྟॖ๙ఃᄝݖॖбइᆔԩ֥หᆘq2(t+1)=q2(t)+A2[X2qᆴѩ০ႨJury่ࡱקॖᆩ:E2(t)+(1-X2)m2(t)]0ູ҂໗קׄ,Վൈ۲ӌഅ`````õ(a-c2-2bq2(t)-bq1(t))֥Ӂਈनູ0,ࣜ࠶࿐ၩၬbE1,E2ູλׄb֒ડቀ၂ק֥Jury่ࡱൈE*൞ࡶ࣍໗ק֥bႨোර֥ٚم,ॖၛ(7)ඹ۱नޙູ࣮ׄᄝܪଆᇏ֥౦ঃb:1`q1ෛሢA1֥э߄ؓб
ֻ11௹``````````ိޠྖ,ᅦٙ:ջൈᇌ֥؟ܪܞ୶ଆࠣః໗קྟ117``1ᇏ໓ང[6]࣮֥ଆᇏӌഅ1֥ӁਈෛA1֥эטᆜҦbࡅӌഅࡎࣩ۬ᆚ൞бࢠૼ֥,ၹՎॉ੮߄ᄝڸ࣍ԛགྷٳҴ,طЧ໓࣮֥ଆᇏӌഅ1ࡅӌഅनҐႨՎҦbࡼt-1ൈ௹֥Ӂཧ൲ਈቔູ֥ӁਈෛA1֥э߄൞ᄝڸ࣍ԛགྷ֥ٳҴགྷའ,іૼҕॉ֥၇ऌࡆೆଆᇏ,ଆ۷ژކൌ࠽bᄵ֤֥֞༢(7)֥ൈᇌቔႨ۷ູૼཁbݓ3G൧ӆ֥ࣩᆚଆູ:M1(t+1)=P1(t)2 带时滞三寡头模型的实际应用及分析M2(t+1)=P2(t)M3(t+1)=P3(t)``2008୍ष,3Gඌषն৯ؿᅚbݓ֥3G๙P1(t+1)=P1(t)+A1(X1P1(t)+(1-X1)M1(t))ྐ൧ӆ൞Ⴎᇏݓ၍aᇏݓ৳๙aᇏݓྐܪ؎֥`````õ(a1-2b1P1(t)+c1P2(t)+d1P3(t))൧ӆ,ࡅ܄ඳ౼֤ਔ҂֥3Gຩ๙ྛᆣ,ٳљູP2(t+1)=P2(t)+A2(X2P2(t)+(1-X2)M2(t))TD-SCDMAaWMCDAaCDMA2000ຩ,ط3G൧ӆ֥ࣩ`````õ(a2+b2P1(t)-2c2P2(t)+d2P3(t))ᆚᇶ֝ൌᇉഈູ൞Ӂࡎ֥ࣩ۬ᆚ,ӁᆭࡗႵ၂ק֥P3(t+1)=P3(t)+A3(X3P3(t)+(1-X3)M3(t))ูսྟb໓ང[5]۳ԛ৳๙֥֥ളӁݦඔ(ࠧ൲ԛݦඔ)ູ:`````õ(a3+b3P1(t)+c3P2(t)-2d3P3(t))Q1£(t)=a1-b1P1(t)+c1P2(t)+d1P3(t)(11)(13)ఃᇏ,a1,b1,c1,d1>0,c1,d1іൕӌഅᆭࡗӁࡎู֥۬֒ଆᇏҕඔ౼ᆴູA2=,A3=,a1=,b1=սӱ؇bPi(i=1,2,3)ູࡎ۬,c1=,d1=,a2=,b2=,c2=,d2۴ऌࡌഡॖၛ֤֞৳๙܄ඳᄝtൈ௹֥০ݦඔູ:=,a3=,b3=,c3=,d3=,X1=X2=01(t)=P1(t)Q£1(t)(12)X3=ൈ,2ູ༢(13)ა҂ॉ੮൧ӆൈᇌ֥ଆ֥``ႮႿ൧ӆྐ༏֥҂ປСྟ,അࡅ߶ॉ੮ҐႨႵཋྟؓбb2`P1ෛሢA1֥э߄ؓб``2іൕ֥൞ໃࡆೆൈᇌൈ৳๙܄ඳෛA1֥э߄߶ᄝ၂؍ൈࡗଽ၂۱܄ඳࠆ০ࠆ֥ն֥ग़,ग़߶۴აࡆೆൈᇌၛު༢(13)ᇏ৳๙܄ඳෛA1֥ؓбэ߄ऌࡎ۬ট࿊ᄴ܄ඳ,൞၂֊ԛགྷࠁᚧགྷའࡎ๋֥۬ݖbభᆀᄝቐႷԛགྷٳҴ,طުᆀࡼఃӾ֞ڸႿَᄵ҂০Ⴟग़ಕ֥໗ק,ં൞ؓႿӌഅߎ൞ग़࣍bॖၛुԛࠁᚧٳҴ֩གྷའӾਔbႮႿ൞૫ؓग़ಕ൞҂০֥bم۴ऌ౦ঃᇅק༯၂֥҄Ҧߎಸၞଢᆰࢤ࿆Ԯ,ԩႿ൧ӆࣩᆚᇏ֥ࡅ܄ඳఃࡎ۬ؓؓ൭ط൞бࢠૼ֥,ࡅ܄ඳᄝࣩᆚᇏѩ҂ି৫ࠧղ֞ବ֥ཊೆࡎ۬ᅞbགྷൌᇏࡅ܄ඳສສ߶Ґ౼ӉႪ߲ᇛनޙׄ,сྶေࣜݖޓ؟֥ѰᒮbၹՎ,֒၂۱ࣩᆚ܄ඳ௹aົ༢ܥקग़ಕaק௹ԛႪ߲ࠃaิۚඌ໗קຩࡆؓࡎ֥۬טᆜ؇ൈ,бೂ৳๙܄ඳ҂؎ԛ۷ྍ۷֩൭؍൧ӆЌӻ໗קbطЧ໓ᇏॉ੮൧ӆ࠺ၫྟࡆೆႪ߲֥สҔ་ႄग़ൈᇌᄵॖၛߏࠁᚧགྷའ֥Ӂള,ܪᆭࡗॖၛ࿃,ႄఏ၍ބྐਆࡅ܄ඳࢆࡎၛؓbೂՎࣼ߶ࣩᆚࡆख,Ֆطԛགྷٳҭࠁᚧ֩གྷའbᆃᇕࣉྛѰᒮࠆ֤০bᆚ౼ਔ۷؟֥ൈࡗটॉ੮ؓҦbؓᆜགྷའ֥ԛགྷؓ۱܄ඳط൞҂০֥b؋ൈࡗটुॖି۱൧ӆط൞Ⴕ০֥b
118༢``۽`ӱ``````````````````2011୍ComputersandMathematicswithApplications,3 结论2009,(57):488j499.Ч໓ࡹ৫ਔᄝטᆜݦඔᇏႄೆൈᇌ֥Ⴕཋྟචܪ[5]`ChenF,MaJH,ଆprocessofthetriopolygamesinchinese3G,๙ݖაԮ֥ଆؓбіૼᄝטᆜҕඔᇏႄೆൈᇌႵི֥ࠁᚧӾbѩࡼᆭܼᄎႨ֞ݓ3G൧ӆ֥telecommunicationmarket[J].Chaos,Solitonsandܪଆᇏ,္֤֞ਔᄝႵཋྟטᆜӌഅᇏൈᇌ֥Fractals,2009,(42):1542j1551.ႄೆᆜ۱༢֥ٳҴࠁᚧӾ֥ࢲં[6]`,ٳ༅ਔࣜ࠶࿐ྛູb๙ݖඔᆴٟᆇဒᆣਔࢲં֥ᆞಒྟbwithboundedrationality[J].MathematicalandComputerModelling,2010,(52):1479j1489.ҕॉ໓ང:[7]`܇Ⴅ,Ϻၬ.҂Ѱᒮܒൔ༯ܪҵၳ߄ࣩᆚބఆ൪קࡎҦ[J].༢۽ӱ,2010,28(4):59j[1]`BischiGI,[M].B[8]`AgizaHN,HegaziAS,:AdvancedinDynamicGamesandApplication,[J].[2]`AhmedE,,2002,(58):[J].ChaosSolitonsFractals,2000,(7):1025j1028[9]`ᅦྍ,ঠૼႧ,ွᄶ.ܪؿഅБࡎଆࠣ.[3]`AgizaHN,HegaziAS,ఃࠁᚧ॥ᇅ[J].༢۽ӱંაൌ,2009,(29):[J].ChaosSolitonsFrac[10]`KebriaeiH,,2001,(9):[J].MathematicsandComputersinSimulation,2011,[4]`AgizaHN,[J(81):1202j1217.].Multi-oligarchCournotCompetitionModelwithTimeDelayandItsStabilityYAOHong-xing,ZHANGFang(JiangsuUniversity,Zhenjiang212013,China)Abstract:Thispaperstudiesmulti-oligarchcournotmodelwithboundedrationalityintowhichtimedelayisincorportedinadjustfunctionbytakingthememoryofthemarketintoconsideration,,,:BoundedRationality;OligarchCompetition;TimeDelay;Chaos;NashEquilibrium
