ֻ25जֻ6௹ଽࡾഽٓ࿐ჽ࿐Б ზ *(蚌埠学院数理系, 安徽 蚌埠 233030) ᅋ ေ:ՖѰᒮච֥ٚႵཋྟԛؿ,ؓႵཋྟචܪѰᒮଆࣉྛਔקਈٳ༅,ѩࡼܪ֥Ӂਈטᆜ؇൪ູఒြ֥ࣩᆚҦ,ࢹᇹඔᆴٟᆇ֥ٚمฐษਆఒြҦӑԛ໗קთު֥০౦ঃ,ѩࡼૌა۲ሱनޙ০ቔбࢠ.ࢲݔіૼູਔሱദ০ၭቋն߄ਆఒြॖၛҐ౼ކቔࣩᆚѰᒮ,ࣜචّٚگѰᒮު൧ӆቋᇔࡼԩႿ໗קनޙ.ܱՍ:ܪ;؎൧ӆ;ఒြࣩᆚ;ކቔࣩᆚѰᒮᇏٳোݼ:F224໓ངѓᆽ:A໓ᅣщݼ:1671-1785(2010)06-0063-04 مݓࣜ࠶࿐ࡅܞ୶ิԛ֥ܞ୶ଆࢠݺֹ૭ඍӆ֥ဆ߄൝,൧ӆ֥ҕაᆀ֥Ҧྛູ[11-12]ؓਔචܪѰᒮࣩᆚ.ಖطܞ୶ଆ֥ࠎЧࡌഡᆭ၂֥႕ཙ۷൞҂ಸޭ൪,ܪѰᒮ൧ӆ۷൞ೂՎ.ሔ൞ྛູದऎႵປಆ,ྟᆃ၂ࡌקႄఏᇭ؟࿐ᆀ֥০ቋն߄֥ਆܪሹ߶ؓሱ֥࠭Ҧҕඔࣉྛטᇉၐ,ૌಪູགྷൌᇏఒြ֥थҦ൞Ⴎದቓԛ֥,ᆜ,චٚѰᒮ֥ࢲݔࡼؓఒြ০Ӂളહဢ֥႕ದႮႿ൳ۋᆩಪ്ି৯ބ࠹ෘି৯ཋᇅ෮ቓԛ֥थཙ,ܪ൧ӆೂޅ,ܪҐ౼હဢ֥ҦҌؓҦ҂ॖି൞ປಆྟ,֥طᆺି൞Ⴕཋྟ֥,Ⴟ൞ሱ࠭ቋႵ০,Ч໓ؓՎࣉྛਔ࣮.ૌࡼႵཋྟනམႄೆ֞ܪѰᒮଆᇏ[1-6].1 ႵཋྟචܪѰᒮଆAgiza֩ದࡼBischi֥ଆቔਔڿࣉ,࣮ࠎႿႵཋྟყ௹֥ऎႵ٤ཌྟӮЧ֥චܪѰᒮଆ,ࡌഡ൧ӆթᄝਆ۱ࣩᆚఒြ,ૌളӁᇕࠣླݦඔڿэൈ֥චܪѰᒮଆ;ૌؿགྷᇉഅ.ഡqi(t)ֻູi(i=1,2)۱ఒြ֥ᄝtൈख़֥֒༢ҕඔэ߄ൈ,൧ӆࡼԛགྷᇛ௹ٳҴaࠁᚧ֩گഅ܂ႋਈ,൧ӆ֥ሹླބሹ܂۳ཌྷ,ᄵֻtൈᄖ৯࿐གྷའ.ၞჅቭ֩[7]ࣉ၂҄ࡼऎၮԛིႋႄ௹൧ӆሹ܂۳Q(t)=q1(t)+q2(t).ഡpູ൧ӆ֥ೆႵཋྟචܪѰᒮଆᇏ,ѩᆷԛܪ֥ྟԛౢࡎ,aູ൧ӆቋۚࡎ,bູ൧ӆ֥ླྟ,൧ӆބၮԛིႋؓ༢൞ڎཟNashनޙࠇཊೆࠁᚧࡎ۬აሹླܱ༢ູp=f(Q)=a-bQ,ఃᇏa,bሑऎႵᇗေ֥႕ཙ.໓[8-10]ӂඍਔऎุ൧ӆᇏູᆞӈඔ.ࣉ၂҄ࡌഡఒြ֥ളӁӮЧູCi(qi)=֥ܪѰᒮଆ,ႨѰᒮંනམᆷ֝ఒြ֥Ӂਈ2ciqi(i=1,2),Ⴟ൞ఃֻt௹֥০ູथҦ.P2i(q1,q2)=pqi(t)-ciqi(t);ഈඍ໓ངն؟Ֆ༢ሹุ֥࢘؇ಀซં၂۱ಒш࠽০ູק༢֥ဆ߄໙,ีᆷԛ֒൧ӆҕඔ౼҂ᆴൈ,ॖ5Pi5pି֝ᇁ༢ࣉೆनޙaᇛ௹മᇀࠁᚧ.ಖط=p+qi(t)-2ciqi(t).(1)5qi5qiૌޓഒิࠣఒြ֥ିቔႨ,གྷൌ֥൧ӆဆ߄ႵཋྟචܪѰᒮଆࡌקఒြᆺऎႵႵཋ൞٤ӈگᄖ,֥൧ӆଽaຓ֥҆۲ᇕၹन႕ཙሢ൧ྟ,ၹطఃളӁथҦ൞ࠎႿሱ࠭གྷ௹ш࠽০* ൬۠ರ௹:2010-03-16 ࠎࣁཛଢ:νߪസۚ֩࿐Ⴊྮౝ୍࢝ഽದҌ॓ሧᇹཛଢ(2010SQRL115) ቔᆀࡥࢺ:ზ(1980-),୯,νߪࠛ༗ದ,Ёҁ࿐ჽࢃഽ,ණൖ,ᇶေՖ൙گᄖ༢ࡹଆაٳ༅,࠹ඔऌԩაٳ༅֩ٚ૫֥࣮.
#64#ଽࡾഽٓ࿐ჽ࿐Бֻ25जֻ6௹ቓԛ.֥ೂݔགྷ௹֥ш࠽০ູᆞ,ఒြࡼᄝ༯၂௹2 ႵཋྟܪఒြࣩᆚҦٳ༅ิۚӁਈ,ّᆭᄵࢆ֮Ӂਈ.ՖطႵ༯ඍ֥Ӂਈטᆜൌ࠽൧ӆᇏ֥ླݦඔཌྷؓಒק֥(a,bཌྷؓଆൔ໗ק),ѩਆఒြ֥ш࠽ӮЧ۵֒ൈඌ่ࡱܱ༢5Piqi(t+1)=qi(t)+vi(qi(t)),i=1,2,(2)ࣅૡ,ཌྷ֒Ӊ၂؍ൈࡗ൞҂э֥(c1,c2ཌྷؓ໗5qiఃᇏק).طӁਈטᆜ؇vi(i=1,2)ಒ൞၂۱۵ఒြ֥,vi(qi(t))൞ؓш࠽০֥טᆜӱ؇,๙ӈ౼ູཌྟݦඔྙൔथҦཌྷܱ,ఒြູਔఽᅝ൧ӆٺحࠣሔۚ০,ෛvi(qi(t))=viqi(t),viູᆞ֥ӈඔ,іൕֻiఒြ֥Ӂਈטᆜ؇,ఃၩၬ൞ളӁൈॖିڿэሱ֥࠭Ӂਈטᆜ؇(Ҧࠏᇅ),෮ၛഅ၇ऌщࠠ০ᄝགྷ௹Ӂਈ֥ࠎԤഈטᆜӁਈ֥бॖࡼvi൪ູఒြࣉ၂҄ิۚ০طҐ౼֥Ҧ.ູ২ਔሔ০ቋն߄,Ⴕཋྟ֥ܪఒြ߶ࢨ؍ྟ.৳ކֹؓሱ֥࠭Ҧviࣉྛטᆜ;ᄝܪѰᒮ൧ӆᇏ,(1)(2)ॖ֤֥֞৯༢ਆࡅఒြൈטᆜҦ,൝с߶႕ཙᆜ۱൧ӆ֥ؿq1(t+1)=q1(t)+v1q1(t)[a-2(b+c1)q1(t)-bq2(t)].ᅚ,ਆࡅࣩᆚ҂֒߶ᄯӮਆϧऒഄ,෮ၛఒြq2(t+1)=q2(t)+v2q2(t)[a-2(b+c2)q2(t)-bq1(t)]ေ҂؎ٳ༅൧ӆߌބሱ֥࠭০౦ঃটथקሱ࠭(3)۴ऌࢳ҂֥ׄٚم[2]֤֞༢(3)֥नޙ֥Ҧ.ູׄ3 ඔᆴٟᆇE0=(0,0),Ea1=(,0),2(b+c1གྷࡌקਆఒြ֥Ҧࠢࠧॖ࿊ᄴთູv1ᇠބv2ᇠܒӮ૫ֻ֥၂འཋ,ഡקචܪ֥ӁਈטEa*2=(0,),E*=*(q1,q2).2(b+c2)ᆜ؇(Ҧ)֥טᆜਫ਼ࣥ,ෛሢӁਈטᆜ؇֥эఃᇏ߄,ܴҳૌ۲ሱ০֥э߄౦ঃ.ࡌഡטᆜਫ਼ࣥٚ*a(b+2c2)q1=σູֆཟטᆜაචཟטᆜ(2).෮໌ֆཟטᆜ,ࠧ2,3b+4b(c1+c2)+4c1c2ܥק၂ࡅఒြ֥Ӂਈטᆜ؇,טࢫਸ਼၂ࡅఒြ֥*a(b+2c1)q2=32.טᆜ؇,ѩܴҳՎൈਆఒြᄝଖൈࡗ؍ഈ֥০b+4b(c1+c2)+4c1c2ഈ૫ඹ۱नޙׄᇏᆺႵE*൞ࠣन০,ѩࡼࢨ؍न০აః۲ሱनޙׄԩNashनޙ,ׄఃჅ֥൞༢֥шࢸनޙׄ.۴ऌJury's่ࡱ[2]࠹ෘ֥০ቔбࢠ.ခሢᆰཌt1აᆰཌt3ࣉྛ֥טᆜ֤ࣼ֞N൞ֆཟטᆜ,ၹᆃਆ่ᆰཌ֥טᆜٚൔোර,༯૫֥ashनޙׄE*֥໗ק่ࡱ(4)ൔ,Ֆط֤ࣼ֞ਔNashनޙׄE*֥໗קთٟᆇݖӱࣇؓt3ࣉྛ࣮.චཟטᆜ൞ᆷਆఒြ.**2ൈטᆜሱ֥࠭Ӂਈטᆜ؇,ѩܴҳՎൈਆఒြᄝ4v1(b+c1)q1+4v2(b+c2)q2-v1v2(3b+**ଖൈࡗ؍ഈ֥০ࠣन০,ѩࡼࢨ؍न০8b(c1+c2)+4c1c2)q1q2-4<0.(4)ഡק൧ӆቋۚࡎ۬a=7,ླྟაః۲ሱनޙׄԩ֥০ቔбࢠ.චཟטᆜ֥ٚൔb=015,ਆࡅఒြ֥ш࠽ӮЧູࢠ؟,Ⴟ໓ᅣږ,གྷࣇၛׅ֥טᆜٚൔູ২ࠧc1=1,c2=2.۴ऌ(4)ൔ֤֞൧ӆनޙ֥ׄ໗קთಞਆఒြ֥Ӂਈטᆜ؇ခሢᆰཌt2ࣉྛטᆜ.(1). 两企业的产量调整速度按单向调整方案进行调节ᄝᆰཌt3ഈ౼ׄE(0108,0105),F(0105,0135),G(01465,0105),ఃᇏૄ֥ׄޘቕѓ֥ඔᆴ൞ᆷఒြ1֥Ӂਈטᆜ؇,ሺቕѓඔᆴ൞ఒြ2֥Ӂਈטᆜ؇.ٳљၛᆃ֥ׄቕѓᆴቔູ൧ӆ֥Ԛ่ࡱ,ܴҳՎൈਆఒြᄝ50~100ൈࡗ؍ഈ֥০ࠣन০,ѩࡼࢨ؍न০აః۲ሱनޙׄԩ০ቔбࢠ(ೂ3~5).ఃᇏ,3ᇏఒြ11ᄝ50~100ൈࡗ؍ഈ֥০aन০aनޙ০ᇗ ൧ӆनޙ֥ׄ໗קთކ,ఒြ2ၧೂՎ.ູਔࡨഒའᇏ֥ሳژඔ,ၛ༯
2010୍6ᄅზ:ܪ؎൧ӆ༯ఒြࣩᆚҦ#65#4 v1=0135,v2=01052 ఒြӁਈטᆜ؇֥ਆᇕטᆜٚσ۲ᇏ౷ཌ֥ݣၬनၛࡥეѓԛ,бೂఒြ1֥০࠺-ູ1֥০.,ఒြ1नޙׄԩ֥০࠺-ູ1֥नޙ০.,ఃژݼၛՎো.ఃᇏ*ཌ)ఒြ1֥नޙ০,oཌ)ఒြ2֥नޙ০;50~100ൈࡗ؍ਆఒြ֥न০Ⴈ#ཌѓൕ. 两企业的产量调整速度按双向调整方案进行调节ᄝᆰཌt2ഈ౼ׄM(0115,0115),N(0134,0134)ބL(014,014),ٳљၛᆃ֥ׄቕѓᆴቔູ൧ӆ֥Ԛ่ࡱ,ܴҳՎൈਆఒြᄝ50~100ൈࡗ؍ഈ֥০ࠣन০,ѩࡼࢨ؍न০აః۲5 v1=01465,v2=0105ሱनޙׄԩ֥০ቔбࢠ(ೂ3a6ބ7).3 v1=0108,v2=0105ࣜၛഈٟᆇ࠹ෘॖၛ֤֞༯૫֥ࢲ:ં6 v1=0134,v2=0134(1)֒ਆఒြ֥ҦܒӮ֥ׄЌӻᄝ໗קთଽ,ᆀᄵၹטᆜ؇ݖն,ሱ֥࠭ࢨ؍न০֮Ⴟఃਆఒြ֥০ࣜ؋ᄠ֥భ௹טᆜު,ቋᇔࡼ߶ཟनޙ০.Վൈ൧ӆཊೆࠁᚧ,ఒြၘمؓໃট໗קनޙ,ࠆ֤֥न০ࢠ.ۚቓԛყҩ.(2)֒၂ࡅఒြ֥Ӂਈטᆜ؇҂նܥק,ෛ(3)֒ਆఒြ֥Ӂਈטᆜ؇ޓն,֤ਆఒሢਸ਼၂ࡅఒြӁਈטᆜ؇֥҂؎ิ,ۚቋᇔਆြҦܒӮ֥ׄӑԛ໗קთൈ,ૌ֥০ѯޓఒြ֥ҦܒӮ֥ׄӑԛ໗קთ,Ҧܥק҂ᆀն,ࢨ؍न০नб۲ሱनޙൈ֥০֮.۵֥ࢨ؍न০აఃनޙ০ཌྷҵ҂ն,ಖطט(ؽ)োර,Վൈ൧ӆၘཊೆࠁᚧ.
#66#ଽࡾഽٓ࿐ჽ࿐Бֻ25जֻ6௹э߄,ൡൈֹטᆜఒြሱദ֥ؿᅚଢѓ,࣐ਈх૧Ӂਈࣩᆚࣉೆࠁᚧ֥҂ॖყҩሑ.ਆܪམࠆ֤ۚ০ႋॉ੮ކቔࣩᆚѰᒮ,൧ӆࣜݖ၂؍ൈࡗטᆜࡼࣉೆ໗קሑ,ᆃࡼႵ০Ⴟఒြሱദ০ၭ,္Ⴕ০Ⴟഠ߶ؿᅚ.ҕॉ໓ང:[1]AhamedE,AgizaHN,'sdynamicalduopoly[J].Chaos,Solitons&Frac-tals,2000(11):1025-1028.[2]AgizaHN,HegaziAS,'smodelwithboundedrationality[J].Chaos,Solitons&Fractals,2001,12(9):1705-1717.7 v1=014,v2=014[3]AgizaHN,ఒြູሔቋն০߶҂؎ڿэሱ֥࠭Ҧ,dynamicsandsynchronizationofaduopolygamewithᆺေਆఒြ֥ҦܒӮ֥ׄಯԩႿ໗קთଽ,ਆboundedrationality[J].,ᆀ০ቋᇔࡼཟ۲ሱ֥नޙ০,ਆఒြ֥Ҧ2002,58(2):133-146.ܒӮ֥ׄӑԛ໗קთ,ਆᆀᇏሹႵ၂۱֥০൳[4]ᤍ,ဗ઼ႇ.ކቔࣩᆚѰᒮᇏ֥گᄖྟაဆ߄नޙ֥໗קྟٳ༅[J].༢۽ӱંაൌ,2004(2):90-94.,бఃनޙׄԩ֥০֮.ਆఒြଢ֥҂؎ᄹնሱ֥࠭Ӂਈטᆜ؇[5]ࣂӔ,ٓࣉ࿐.ᇗگѰᒮᇏҕაᆀथҦྛູ֥ࣜ࠶࿐,ఒြ҂ࣇ҂ିࠆ֤ۚ০ࢳ[J].෬,2005(6):4-7.,ط߶൧ӆཊೆࠁᚧ,ᄯӮਆϧऒഄ.[6]ზ,ࡉӔႧ.҂ྟචܪѰᒮଆ֥گᄖྟٳሸഈ෮ඍ,ھ໓ؓႵཋྟචܪѰᒮଆࣉ༅[J].گᄖ༢აگᄖྟ॓࿐,2007,4(2):71-76.ྛਔקਈٳ༅,ѩؓ໗ק൧ӆߌ༯ܪّگѰᒮ[7]ၞჅቭ,ഹᅲᜧ,่फ.ऎၮԛིႋ֥Ⴕཋྟචܪު֥০౦ঃࣉྛਔབྷ༥֥ඔᆴٟᆇ.ࢲݔіૼ,Ⴕ֥ဆ߄[J].༢۽ӱ࿐Б,2004,19(3):244-250.ཋྟචܪ֥Ӂਈטᆜ؇(ఒြҦ)҂౼ᆴ[8]ိޠྖ,ྷڂ.චܪႵཋྟܼۡѰᒮଆ֥گᄖྟؓఒြቋᇔ০߶Ӂളᇗေ႕ཙ,֒ਆఒြҐႨٳ༅[J].༢۽ӱંაൌ,2005,25(12):32-37.ࢠ֥֮טᆜ؇ൈ,ච֥ٚ০ࣜ؋௹ѯުቋᇔ[9]ӧۚႳ.ഈ൧܄ඳѩܓקࡎѰᒮଆ[J].ඹԫഽٓն࿐Ⴟनޙ০,ปਆఒြᇏ၂ٚҐႨޓ֥ۚטᆜ࿐Б,2007,34(2):34-37.؇ൈ[10]ᅦਅ.ဆ߄Ѱᒮනམ֥ᇅ؇ٳ༅:ᇏݓࣜ࠶ሇ࣮֥,ਆఒြ֥০ቋᇔࣉೆखਛѯሑࠧࠁᚧ,ط၂֊൧ӆࣉೆ֞ࠁᚧྍ൪࢘[J].ඹԫഽٓն࿐࿐Б,2008,35(3):31-36.,ఒြࡼمؓӉ௹[11]౮.ଽࡾ൧ᇏཬఒြҍༀາࠏܵҦ࣮[J].֥ӁਈथҦࣉྛყҩטᆜ.෮ၛ,ؓႿऎႵႵཋྟଽࡾഽٓ࿐ჽ࿐Б,2008,23(ᄹ):283-285.֥චܪఒြѰᒮ,ေ҂؎ֹᇿၩఒြ෮ԩ֥ߌ[12]ჯౝ,ွන,ޱౖ,֩.ଽࡾ߲ԫӑ൧ႏཧҦ࣮[J].ଽࡾഽٓ࿐ჽ࿐Б,2009,24(S2):-rong(DepartmentofMathsandPhysics,BengbuCollege,Bengbu,Anfei233030,China) Abstract:Startingofffromtheboundedrationalityoftwogameplayers,,andafteralongtimeofgamingbetweenthetwosidesthemarketwouldgraduallystikeabalancedstateofequilibrium. Keywords:oligopolisticmarkets;boundedrationality;duopoly;cooperative-competitivegamingstrategy(ᄳщࠠ:胡 蓉)
