ꆡ2001쓪8퓂쾵춳릤돌샭싛폫쪵볹뗚8웚ꆡ컄헂뇠뫅:100026788(2001)0820034203ퟓ늩?뺫솶쓉쪲뻹뫢럇뻹뫢슷뺶벫킡벫듳뮯뺫솶램뚡햼컄(붭쯕샭릤듳톧샭톧풺,붭쯕헲붭212013)햪튪:ꆡ룸돶뻹뫢뺫솶뗄벫킡벫듳뮯ힼ퓲,퓚ퟓ늩?뺫솶쓉쪲뻹뫢럇뻹뫢슷뺶짏뛔뻹뫢닟싔뷸튻늽뺫솶톡퓱Λ맘볼듊:ꆡퟓ늩?뺫솶쓉쪲뻹뫢;럇뻹뫢슷뺶;벫듳벫킡뮯ힼ퓲훐춼럖샠뫅:ꆡO225ꆡꆡꆡ컄쿗뇪쪶싫:ꆡAꆡꆡꆡꆡꆡꆡꆡꆡαMinimum2MaximumMethodofRefiningtheSubgamePerfectNash2equilibriumontheOut2of2EquilibriumPathDINGZhan2wen(FacultyofScience,JiangsuUniversityofScienceandTechnology,Zhenjiang212013,China)Abstract:ꆡ:ꆡsubgameperfectNash2equilibrium;out2of2equilibriumpath;minimum2maximumcriterion1ꆡ틽퇔늩?럖컶뗄쒿뗄쫇룸돶늩?뗄뻹뫢뷢,풤닢늩?뗄뷡맻.늩?싛뗄랢햹맽돌훐,룷훖훘튪뗄믹놾뗄뻹뫢뷢뗄룅쓮뚼뫜쓑퓚놣횤듦퓚탔뗄춬쪱놣횤캨튻탔,평듋닺짺뗄뻹뫢뛠훘탔컊쳢쫇늩?싛쏦쇙뗄튻룶쓑쳢Λ뷢뻶뻹뫢뛠훘탔컊쳢뗄훷튪랽램쫇퓚튻훖뻹뫢룅쓮훐,샻폃쳘뚨뗄움볛ힼ퓲뷸튻늽럖뇦돶웤훐쓄킩쫇뷏뫏샭뗄,쓄킩쫇늻첫뫏샭뗄,듓뛸듓뛠훘뷢훐쳞돶늻짵뫏샭뗄쓇킩뷢Λ헢훖랽램놻돆캪뻹뫢뗄뺫솶Λ췪좫탅쾢뚯첬늩?훐,ퟓ늩?뺫솶쓉쪲뻹뫢뻍쫇퓚쓉쪲뻹뫢훐뺫솶쳴톡뗄퓚쎿룶ퟓ늩?짏뚼릹돉쓉쪲뻹뫢뗄튻훖럻뫏탲맡샭탔뗄뻹뫢Λ떫ퟓ늩?튪쟳듓떥뷡탅쾢벯뾪쪼,쟒늻쓜럖룮탅쾢벯,헢훖쿞훆쪹뗃탭뛠뫳탲늩?늿럖뗄닟싔늻쓜뷸튻늽뺫솶(볻컄훐샽ퟓ늿럖)Λ놾컄룸돶뗄뺫솶룅쓮폫랽램,쫔춼퓚쯹폐럇뻹뫢슷뺶짏뛔ퟓ늩?뺫솶쓉쪲뻹뫢뷸튻늽뷸탐뺫솶쳴톡Λ2ꆡ볇뫅뾼싇n죋췪좫탅쾢뚯첬폐쿞늩?G={Hi;Ai;Si;ui;i=1,2,ꆭ,n},웤훐Hi쫇닎폫죋i뗄탅쾢벯뗄벯뫏(늩?쫷쏨쫶훐,탅쾢벯쫇튻킩뻶닟뷡뗄벯뫏),Ai=ꇈA(hhꇊi)캪닎폫죋i뗄탐뚯뿕볤,A(hi)쫇웤퓚탅Hii쾢벯hi짏뗄탐뚯벯뫏,Si={siûsiꇊꇁhꇊA(hi)}캪닎폫죋i뗄뒿닟싔뿕볤,siꇊꇁhꇊA(hi)쫇닎폫죋i뗄튻룶뒿HHiiii닟싔,ui(s)>ui(s1,s2,ꆭ,sn)쫇퓚닟싔ퟩ뫏s=(s1,s2,ꆭ,sn)쿂닎폫죋i뗄횧뢶Ζ헢쫇췪좫탅쾢뚯첬늩?뗄닟싔쪽쏨쫶Ζ놾컄퓙틽뷸죧쿂볇뫅Ζα쫕룥죕웚:1999212216' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
뗚8웚ퟓ늩?뺫솶쓉쪲뻹뫢럇뻹뫢슷뺶벫킡벫듳뮯뺫솶램35H=ꇈnHi뇭쪾룃늩?쯹폐닎폫죋쯹폐탅쾢벯뗄벯뫏,i(h)뇭쪾퓚H훐탅쾢벯h짏뻶닟뗄닎폫죋,듓i=1뛸폐쟒뷶폐닎폫죋i(h)퓚h짏톡퓱탐뚯ΖGT(h,x)뇭쪾듓탅쾢벯h짏뻶닟뷡x뾪쪼뗄뫳탲늩?(헢쪱웰뗣x쫇GT(h,x)뗄떥뷡탅쾢벯),ui(h)(sûh,x)>ui(h)(s1,s2,ꆭ,snûh,x)뇭쪾닟싔ퟩ뫏s=(s1,s2,ꆭ,sn)쿂늩?GT(h,x)좷뚨뗄닎폫죋i(h)뗄횧뢶Ζn(h)=#h뇭쪾h짏뻶닟뷡뗄쫽쒿,nA(h)=#A(h)뇭쪾(닎폫죋i(h)퓚탅쾢벯h짏뿉톡탐뚯뗄쫽쒿Ζa(h)뇭쪾h짏뗄튻룶뿉톡탐뚯s,벴a(h)ꇊA(h).a(h)뇭쪾닟싔ퟩ뫏s=(s1,s2,ꆭ,sn)퓚h짏(닎폫죋i(h))톡퓱뗄탐뚯,s(a(h))뇭쪾뛔닟싔ퟩ뫏s퓚탅쾢벯h짏폃탐뚯톡퓱as(h)듺쳦a(h)뛸뗃떽뗄탂뗄닟싔ퟩ뫏Ζ3ꆡ벫킡벫듳뮯뺫솶램룸뚨뒿닟싔ퟩ뫏s=(s1,s2,ꆭ,sn)뫍탅쾢벯hΖ뛔h짏탐뚯벯뫏A(h)훐뗄쎿룶탐뚯a(h),ui(h)(s(a(h))ûh,x),xꇊh쫇튻룶n(h)캬쿲솿,붫웤럖솿내듓킡떽듳업탲(쿠뗈쪱죎틢업탲)뫳볇캪ꇺui(h)(s(a(h))ûh),돆캪평닟싔ퟩ뫏s좷뚨뗄(닎폫죋i(h))퓚탅쾢벯h짏맘폚탐뚯톡퓱a(h)뗄횧뢶쿲솿Ζ뚨틥1(벫킡벫듳뮯ힼ퓲)ꆡ돆탅쾢벯h짏(닎폫죋i(h))뗄탐뚯톡퓱3a(h)맘폚닟싔ퟩ뫏s싺ퟣ벫킡벫듳뮯ힼ퓲,죧맻뛔쯹폐a(h)ꇊA(h),뚼폐ꇺꇺui(h)(s(a3(h))ûh)σui(h)(s(a(h))ûh)웤훐ꆰσꆱ뇭쪾솽쿲솿내ퟖ뗤탲뇈뷏듳킡(뫳컄춬틥ꇺ,샽죧ꇺu1;u2뇭쪾쿲솿ꇺu1내ퟖ뗤탲업퓚ꇺu2횮뫳)Ζ뚨틥2(럇뻹뫢슷뺶벫킡벫듳뮯쓉쪲뻹뫢33)ꆡ튻룶쓉쪲뻹뫢3s=(s1,s2,ꆭ3,sn)돆캪벫킡벫듳뮯뺫솶뗄,죧맻쯼좷뚨뗄럇뻹뫢슷뺶짏쎿룶탅쾢벯h(닎폫죋i(h))뗄탐뚯톡퓱3sa(h)맘폚3s싺ퟣ벫킡벫듳뮯ힼ퓲Ζ뚨틥3(벫킡벫듳뮯샭탔ퟓ늩?뺫솶쓉쪲뻹뫢)ꆡ튻룶쓉쪲뻹뫢3s돆캪벫킡벫듳뮯샭탔ퟓ늩?뺫솶뗄,죧맻쯼볈쫇ퟓ늩?뺫솶쓉쪲뻹뫢,폖쫇벫킡벫듳뮯뺫솶뗄Ζ듓뚨틥쏷쿔뗘뾴돶,벫킡벫듳뮯뺫솶랽램쫇뛔럇뻹뫢슷뺶뷸탐뺫솶뗄Ζ퓚뻹뫢닟싔3s쿂,럇뻹뫢슷뺶짏뗄탅쾢벯쫇늻쓜떽듯뗄Ζ벫킡벫듳뮯뺫솶램튪쟳뫏샭뗄뻹뫢튲펦룃퓚늻쓜떽듯뗄탅쾢벯짏ퟶ돶뷏뫃뗄낲업Ζퟓ늩?뺫솶튲쫇튪쟳퓚룷룶ퟓ늩?짏ퟶ돶ퟮ폅낲업,떫뛔ퟓ늩?뗄릹돉튪쟳맽룟(튪쟳듓떥뷡탅쾢벯뾪쪼),쯼늻쓜뛔쎿튻룶럇뻹뫢슷뺶짏뗄탐뚯톡퓱뚼뷸탐뺫솶(볻뫳컄샽ퟓ)Ζ벫킡벫듳뮯뺫솶램퓚튻뚨돌뛈짏쏖늹쇋헢훖늻ퟣ,쯼뺫솶뗄탅쾢벯뾪쪼뗄뫳탲늩?뿉틔듓뛠뷡탅쾢벯뾪쪼Ζ퓚ퟷ폅뮯뾼싇쪱,쯤좻탅쾢벯캴떽듯,떫퓚ퟮ뮵뗄쟩뿶훐낲업ퟮ뫃뗄탐뚯톡퓱늻쪧캪튻훖샭탔탐캪Ζ쿂쏦뗄쏼쳢쓜릻쮵쏷헢훖뺫솶랽램퓚튻뚨틢틥쿂쫇뫏뫵샭탔뗄Ζ쿈틽죫튻룶뚨틥Ζ뚨틥4ꆡh짏(닎폫죋i(h))뗄탐뚯ꆫa(h)돆캪맘폚닟싔ퟩ뫏s뗄퇏룱폅뎬탐뚯,죧맻뛔쎿룶a(h)ꇊA(h),a(h)ꇙꆫa(h),뚼돉솢쿲솿늻뗈쪽(솽쿲솿뗄럖솿뚼내xꇊh뗄춬튻쮳탲업쇐)ꆫ(ui(h)(s(a(h))ûh,x),xꇊh)>(ui(h)(s(a(h))ûh,x),xꇊh)웤훐쒳킩럖솿뿉틔좡뗈뫅,떫훁짙폐튻룶퇏룱듳폚돉솢,볇캪ꆫsa(h)>A(h).랴횮돆ꆫa(h)맘폚s뗄쇓탐뚯,죧맻뛔쎿룶a(h)ꇊA(h),a(h)ꇙꆫa(h),뚼돉솢쿲솿늻뗈쪽ꆫ(ui(h)(s(a(h))ûh,x),xꇊh)ꇜ(ui(h)(s(a(h))ûh,x),xꇊh)늢쟒훮쿲솿늻뗈쪽훐훁짙폐튻룶퇏룱킡폚돉솢,볇캪ꆫa(h)ꇜsA(h).쏼쳢ꆡ짨탅쾢벯h퓚벫킡벫듳뮯뺫솶쓉쪲뻹뫢3s=33(s1,s2,ꆭ3,sn)뗄럇뻹뫢슷뺶짏,퓲쿂쇐쫂쪵돉솢3sꆫ1)떱ꆫa(h)>A(h),뇘폐3sa(h)=a(h),ꆫ2)떱a(h)ꇜ3sA(h),뇘폐3sa(h)ꇙꆫa(h).횤쏷ꆡꇺui(h)(s(a(h))ûh)쫇내듓킡떽듳업탲뗄횧뢶쿲솿,평폚업탲뫳쿲솿볤뗄듳킡맘쾵늻뇤,떱ꆫ3sa(h)>' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
36쾵춳릤돌샭싛폫쪵볹2001쓪8퓂A(h)믲ꆫa(h)ꇜ3sA(h)돉솢쪱,뇘폐ꇺꇺu3ꆫ3i(h)(s(a(h))ûh)>ui(h)(s(a(h))ûh),a(h)ꇊA(h),a(h)ꇙꆫa(h)믲헟ꇺꆫu3i(h)(s(a(h))ûh)ꇜꇺu3i(h)(s(a(h))ûh),a(h)ꇊA(h),a(h)ꇙꆫa(h)뫳튻ퟩ늻뗈쪽훐훁짙폐튻룶δa(h)ꇊA(h)퇏룱킡폚돉솢Ζ떱ꆫ3s3sa(h)>A(h)쪱,죴a(h)ꇙꆫꇺ33ꇺs3ꆫ3a(h),퓲ui(h)(s(a(h))ûh)<ui(h)(s(a(h))ûh),듓뛸룼폐ꇺui(h)(s3ꇺ3s3ꆫ3ꆫ(a(h))ûh);ui(h)(s(a(h))ûh),헢폫s뗄벫킡벫듳뮯뺫솶쎬뛜Ζ떱ꆫaꇜsA(h)쪱,죴3sa(h)=a(h),퓲튲폐ꇺ33ꇺs3δui(h)(s(a(h))ûh);ui(h)(s(a(h))ûh)뗄쎬뛜Ζ횤뇏Ζ4ꆡ샽ퟓ샽1ꆡ뾼싇늩?쫷(1),쯼폐솽룶뒿닟싔쓉쪲뻹뫢3s1=(A,{a,b})벰3s2=(A,{a,c})Ζ평폚ퟓ늩?횻폐풭늩?벰듓닎폫죋2ퟳ뇟떥뷡탅쾢벯뾪쪼뗄뫳탲늩?,쿔좻헢솽룶쓉쪲뻹뫢뚼쫇ퟓ늩?뺫솶쓉쪲뻹뫢Ζ뻹뫢3s2=(A,{a,c})뇭쪾닎폫죋1톡퓱탐뚯A,닎폫죋2퓚ퟳ뇟떥뷡탅쾢벯톡퓱탐뚯a,폒뇟쮫뷡탅쾢벯톡퓱탐뚯좷뚨뗄닎폫죋2퓚쮫뷡탅쾢벯h짏맘폚탐뚯c뗄횧뢶쿲솿캪(0,0),맘폚탐뚯b뗄횧뢶쿲솿쫇(0,5),(0,0);(0,5),쯹틔탐뚯c맘폚3s2늻싺ퟣ벫킡벫듳뮯ힼ퓲3,s2늻쫇벫킡벫듳뮯샭탔뗄Ζ3s1쫇룃늩?캨튻뗄뒿닟싔벫킡벫듳뮯샭탔ퟓ늩?뺫솶쓉쪲뻹뫢Ζ쫂쪵짏,닎폫죋2쮫뷡탅쾢벯짏뗄탐뚯b쫇폅뎬뗄,쯤좻룃탅쾢벯늻퓚솽룶뻹뫢뗄뻹뫢슷뺶짏,떫톡퓱폅뎬탐뚯b닅쫇샭탔뗄Ζ쪵볊늩?쪱,닎폫죋1죧맻톡퓱쇋B믲C,탐뚯b뗄톡퓱폐뿉쓜죃닎폫죋2믱뗃횧뢶5뛸늻쿳탐뚯c뗄톡퓱붫떼훂튻컞쯹믱Ζ닎폫죋톡퓱탐뚯BꆢC쫇뿉쓜뗄,틲캪쯼뗄쯰쪧ퟮ뛠캪1Ζ죧맻뛾죋퓚늩?췢뮹폐웤쯼샻틦돥춻,닎폫죋1캪쇋듲냜닎폫죋2,쯻폃튻떥캻뗄샻틦쯰쪧떼훂닎폫죋2뗄뻞듳쯰쪧쫇뿉쓜뗄,쳘뇰퓚늻릫욽짌튵뺺헹훐Ζ춼1샽2ꆡ늩?쫷(2)폐쯄룶쓉쪲뻹뫢33s1=3(a1,b1,c1),s2=3(a1,b2,c1),s3=(a1,b1,c2),s4=(a1,b2,c2).돽풭늩?놾짭췢,컞웤쯼ퟓ늩?,맊쯄룶뚼쫇ퟓ늩?뺫솶쓉쪲뻹뫢Ζ떫쫇닎폫죋3탅쾢벯짏뗄탐뚯c2맘폚죎뫎닟싔ퟩ뫏뚼쫇쇓탐뚯Ζ쯹틔뫳솽룶뻹뫢늻쫇벫킡벫듳뮯샭탔뗄Ζ33s1,s2좷뚨뗄닎폫죋2탅쾢벯짏맘폚탐뚯b1뗄횧뢶쿲솿뚼쫇(5,5),맘폚탐뚯b2뗄횧뢶쿲솿뚼쫇(0,8),평폚(5,5):(0,8),쯹틔3s1=(a1,b1,c1)쫇룃늩?캨튻싺ퟣ벫킡벫듳뮯샭탔뗄ퟓ늩?뺫솶쓉쪲뻹뫢Ζ(쿂뗚62튳)' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
62쾵춳릤돌샭싛폫쪵볹2001쓪8퓂탸뇭2ꆡ뗧뚯훺솦웷쪧킧맊헏쫷뿉뾿탔쒣쓢솽훖쯣램퓋쯣뷡맻뫍킧싊뇈뷏뷡릹몯쫽춨즨맊헏쫷쒣쓢쯣램쪧킧쪱볤몯쫽춨즨맊헏쫷쒣쓢쯣램탲뫅MTBF뗣맀볆횵뇩샺맊헏쫷(떥캻:킡쪱)듎쫽퓋탐쪱볤MTBF뗣맀볆횵뇩샺맊헏쫷(떥캻:킡쪱)듎쫽퓋탐쪱볤럖쏫럖쏫럖쏫럖쏫럖쏫럖쏫럖쏫럖쏫럖쏫럖쏫욽뻹럖쏫럖쏫ꆡꆡ뇭2쿔쪾뗄퓋쯣뷡맻뇭쏷,틔쪧킧쪱볤몯쫽뗄뿉뾿탔쒣쓢쯣램퓚좷놣쒣쓢뷡맻폫뷡릹몯쫽쒣쓢쯣램퓋쯣뷡맻튻훂탔뗄춬쪱,뷏뷡릹몯쫽램퓚퓋쯣쯙뛈짏뻟폐쏷쿔뗄폅쫆Λ6ꆡퟜ뷡놾컄퓚웊컶뷡릹몯쫽춨즨맊헏쫷뿉뾿탔쒣쓢쯣램뗄믹뒡짏,춻웆쇋뒫춳뗄틀뻝쿂튻쫂볾퓶솿램살햹뾪쒣쓢뗄뻖쿞,뛸쫇횱뷓듓탨쟳뷢뗄컊쳢돶랢ퟛ뫏펦폃싟벭쏅뗄쪱볤쳘탔,쳡돶쇋쪧킧쪱볤몯쫽펦폃폚맊헏쫷뿉뾿탔쒣쓢훐,늢듓헻쳥폫뻖늿뗄뷇뛈쳡돶틔맊헏쫷떥뗷쒣뿩럖룮뗄믬뫏쯣램살햹뾪뛔럇떥뗷쾵춳뿉뾿탔쒣쓢퇐뺿Λ쪵볹뫍샭싛럖컶뇭쏷,탂뗄쯣램퓚쾵춳뿉뾿탔쒣쓢훐,쳘뇰쫇퓚떥뗷쾵춳훐,쪡좥쇋뛔뗗쫂볾쪧킧쪱볤뗄업탲뫍랴뢴볆쯣뷡릹몯쫽쪱뛔맊헏쫷뛠듎뇩샺퓋쯣,퓚돌탲짨볆짏룼캪볲뷠,퓚퓋쯣쯙뛈짏룼캪뿬뷝Λ닎뾼컄쿗:\[1\ꆡ]퇮캪쏱,쪢튻탋.쾵춳뿉뾿탔쫽ퟖ쒣쓢[M\].놱뺩:놱뺩몽뿕몽쳬듳톧돶냦짧,1990.\[2\ꆡ]쎷웴훇,쇎뺼짺,쯯믝훐.쾵춳뿉뾿탔릤돌믹뒡[M\].놱뺩:뿆톧돶냦짧.1992.\[3\ꆡ]태뮳타.쾵춳뿉뾿탔쏉쳘뾨싞램풤닢럖컶죭볾뗄짨볆[D\].훐맺몽쳬믺뗧벯췅302쯹,1999.(짏뷓뗚36튳)ꆡꆡퟮ뫳쮵쏷튻뗣,놾컄뷩짜뗄랽램횼퓚뷸늽쳞돽튻킩횱맛짏늻첫뫏샭뗄ퟓ늩?뺫솶쓉쪲뻹뫢,뿉쓜믡돶쿖쎿룶ퟓ늩?뺫솶쓉쪲뻹뫢뚼컞램싺ퟣ벫킡벫듳뮯샭탔뗄쟩뿶,쯹틔튲뿉틔뾼싇냑횧뢶쿲솿훐럖솿볓좨욽뻹퓱폅뗈랽램,헢쪵볊짏뻍튪쟳닎폫죋퓚쯻뗄탅쾢벯뗄뻶닟뷡짏뢳폨룅싊럖늼,컊쳢뻍뮯캪뺫솶놴튶쮹뻹뫢뗄쳖싛Λퟷ헟죏캪,죧맻싺ퟣ쒳훖횱맛샭탔ힼ퓲뗄뒿닟싔쓉쪲뻹뫢듦퓚,폖쫇ퟓ늩?뺫솶뗄,헢훖뻹뫢볈볲떥쫊폃폖늻쪧뫏샭탔Λ닎뾼컄쿗:\[1\ꆡ]헅캬펭1늩?싛폫탅쾢뺭볃톧[M]1짏몣:짏몣죽솪쫩뗪,짏몣죋쏱돶냦짧,19961\[2\ꆡ]헅쫘튻1쿖듺뺭볃뛔닟싛[M]1놱뺩:룟뗈뷌폽돶냦짧,19981\[3\ꆡ]십뚡J냂쮹놾,낢샯뛻ꆤ슳뇶쮹첹.늩?싛뷌돌[M\].캺폱룹틫.놱뺩:훐맺짧믡뿆톧풺돶냦짧,2000.\[4\ꆡ][M\].London:HarvesterWheatsheafPublisher,1992.' 1995-2005 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.
