믆ꆡ쳎:엄싴춶뇪훐뗄싴랽룉죅닟싔럖컶엄싴춶뇪훐뗄싴랽룉죅닟싔럖컶믆ꆡ쳎(놱뺩듳톧맢뮪맜샭톧풺ꆡ100872)ꆡꆡ쓚죝쳡튪:놾컄쳖싛쇋엄싴춶뇪늩?훐싴랽춨맽듺샭죋살룉죅춶뇪엄싴맽돌뗄솽훖닟싔,쟸럖쇋싲랽늻쓜뇦뇰뫍쓜뇦뇰싴랽듺샭죋샠탍뗄솽훖탅쾢볙뚨,평듋쳖싛쇋싴랽듺샭죋뛔엄싴춶뇪뷡맻닺짺뗄펰쿬,웤뷡맻쫇듋쪱쫕틦뗈볛뚨샭늻퓙돉솢ꆣ헢튻쒣탍뿉틔폃살뷢쫍쿖쪵훐뎣뎣랢짺뗄튻훖싴랽닟싔탔탐캪ꆣ맘볼듊:엄싴ꆡ춶뇪ꆡ늩?ꆡ닟싔ꆡꆡퟔVickrey(1961)쫗쿈뛔엄싴춶뇪(auction)뷸탐맦랶럖컶틔살,헢튻쇬폲뗃떽쇋맣랺뗄쳖싛ꆣ웤훐ퟮ훘튪뗄돉맻횮튻쫇쫕틦뗈볛뚨샭(Myerson,1981;RileyandSamuelson,1981)ꆣ헢튻뚨샭쮵쏷,퓚쿠떱뿭랺뗄짨뚨쳵볾쿂,쯄훖엄싴춶뇪믺훆훐싴랽뗃떽뗄웚췻쫕틦뚼쫇쿠뗈뗄ꆣ듋뫳뗄탭뛠퇐뺿컄쿗뾼달쇋쪲쎴쪱뫲헢튻뚨샭뗄뷡싛볌탸돉솢,뛸쪲쎴쪱뫲헢튻뚨샭쪧킧ꆣ웤훐뗄튻훖쮼슷쫇틽죫싲랽횮볤뗄뒮춨(샽죧GrahamandMarshell,1987;McAfeeandMcMillan,1992),듋쪱싲랽쓜뫏쒱춻웆쫕틦뗈볛뚨샭뗄풼쫸,듯떽뛔쯻쏇룼뫃뗄뷡맻ꆣ좻뛸,쇭튻훖쿖쿳튲쫇쿖쪵훐뫜뎣볻뗄닟싔탔탐캪,싴랽뎣뎣뿉틔춨맽튻룶듺샭죋살룉죅엄싴춶뇪뗄맽돌,듓뛸듯떽뛔ퟔ벺룼폐샻뗄돉맻ꆣ샽죧퓚펢쪽엄싴훐,폐쪱뫲싴랽믡춨맽튻룶듺샭죋살닎폫뺺볛,횻튪뻵뗃쿖퓚뗄ퟮ룟돶볛헟뮹폐쳡볛뗄뿕볤,뻍춨맽돶볛뇆돶룼룟볛룱,듓뛸쪹싴랽뗄웚췻쫕틦쳡룟ꆣ놾컄뛔싴랽뗄헢훖탐캪뷸탐늩?럖컶,쮵쏷헢훖닟싔탔탐캪뗄킧맻퓚늻춬뗄엄싴춶뇪믺훆훐킧맻늻춬,쫕틦뗈볛뚨샭뗄뷡싛듋쪱늻돉솢ꆣ튻ꆢ믹놾쒣탍짨뚨컒쏇쪹폃Vickrey뗄늩?쒣탍ퟷ캪믹뒡ꆣ볙짨퓚튻룶뇪뗄뗄엄싴믲춶뇪훐,폐n룶럧쿕훐탔뗄싲랽,쇮vi캪싲랽i뗄놣쇴볛룱,튲뻍쫇쯻뛔뇪뗄뗄맀볛ꆣ웤뻟쳥쫽횵쫇쮽폐탅쾢,컒쏇볙짨릫릲횪쪶쫇vi살ퟔ뛀솢뗄[0,1]쟸볤짏뻹퓈럖늼ꆣ퓚헢훖믹놾늩?볙짨쿂,Vickrey틔벰웤쯻엄싴춶뇪뗄퇐뺿헟뾼달쇋쯄훖춶뇪믺훆:펢쪽엄싴ꆢ뫉삼엄싴ꆢ뗚튻볛룱쏜럢춶뇪뫍뗚뛾볛룱쏜럢춶뇪,룷ퟔ맦퓲폫늩?뻹뫢죧쿂:퓚펢쪽엄싴훐,볛룱횻짽늻붵,돶볛ퟮ룟뗄싲랽믱뗃뇪뗄,횧뢶웤돶볛,퓚맽돌훐퓊탭뛠듎돶볛ꆣ퓚헢훖쟩뿶쿂뫜죝틗뾴떽싲랽뗄ퟮ폅닟싔쫇,죧맻떱잰ퟮ룟볛쫇뇰죋쯹돶뛸쟒뗍폚ퟔ벺뗄놣쇴볛룱,퓲쳡돶룼룟뗄돶볛ꆣ헢훖닟싔뗄ퟮ폅탔뛔튻냣뗄럖늼튲뚼돉솢,ퟮ뫳뗄뻹뫢뷡맻쫇,맀볛ퟮ룟뗄싲랽믱뗃뇪뗄,뢶돶뗄볛룱쫇듎룟맀볛(vi훐뗚뛾룟뗄튻룶)ꆣ뫜쏷쿔,웤쯻뗄싲랽뚼믡춣쇴퓚듎룟맀볛횮잰믲횮짏,틲듋쎻폐죋믡폫맀볛ퟮ룟헟퓚듎룟맀볛횮짏뺺헹ꆣ헢쪱싴랽뗄웚췻쫕틦쫇쯹폐싲랽맀볛훐듎룟맀볛뗄웚췻횵,떱vi럾듓[0,1]쟸볤짏뻹퓈뛀솢춬럖늼쪱,헢튻듎룟맀볛뗄웚췻횵캪(n-1)Π(n+1)ꆣ틲듋펢쪽엄싴뗄싴랽웚췻쫕틦캪(n-1)Π(n+1)ꆣ퓚뫉삼엄싴훐,볛룱듓ퟮ룟뗣훰늽쿲쿂붵뗍,횻튪폐튻룶죋뛔떱잰볛룱뇭쪾뷓쫜,엄싴벴룦뷡쫸,룃죋틔춣횹쪱뗄볛룱믱뗃뇪뗄ꆣ뛔쯼뗄럖컶튻냣폫뗚튻볛룱쏜럢춶뇪뫏늢뷸탐ꆣ퓚뗚튻볛룱쏜럢춶뇪훐,쎿룶싲랽퓚맦뚨뗄웚쿞횮볤쳡붻쏜럢뗄뇪쫩,퓚뾪뇪횮죕춬쪱듲뾪,돶볛ퟮ룟헟믱뗃90
2005쓪뗚7웚뇪뗄,횧뢶춶뇪볛룱ꆣ퓚퇐뺿컄쿗훐,뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪뎣뎣돆캪쫇닟싔뗈볛뗄,풭틲쫇퓚헢솽훖믺훆훐,싲랽뗄닟싔뾼싇쫇뗈볛뗄,뚼쫇쫂잰탨튪좷뚨튻룶볛룱pi,뚼횻폐튻듎뇭듯뗄믺믡,뚼쫇쯹뚨볛룱ퟮ룟헟틔룃볛룱믱뗃뇪뗄,쪵볊짏뿉틔뇭쫶캪춬퇹뗄닟싔탍늩?ꆣ퓚쿠펦닟싔탍늩?뻖쫆뗄뛔돆뻹뫢훐,쎿룶싲랽뗄볛룱닟싔쫇웤맀볛뗄몯쫽pi=f(v)i,짨f뗄랴몯쫽캪g,퓲싲랽뗄웚췻쫕틦캪n-1u)(i=[g(pi]vi-p)i,튲뻍쫇횻폐퓚웤쯻뛔쫖쏇뗄맀볛뗍폚ퟔ벺맀볛쪱ퟔ벺닅쓜믱뗃뇪뗄,퓚vi럾듓뻹퓈럖늼뗄쟩뿶쿂,컒쏇뿉쟳뗃뻹뫢닟싔캪n-1pi=nviꆣ틲듋싴랽뗃떽뗄웚췻쫕틦뻍쫇ퟮ룟맀볛뗄(n-1)Πn놶,뛸뻹퓈럖늼훐ퟮ룟맀볛웚췻캪nΠ(n+1),쯹틔헢솽훖늩?믺훆훐싴랽뗄웚췻쫕틦튲쫇(n-1)Π(n+1)ꆣ퓚뗚뛾볛룱쏜럢춶뇪훐,뫍뗚튻볛룱쏜럢춶뇪뗄맽돌쿠춬,떫ퟮ뫳뷡맻늻춬,돶볛ퟮ룟헟죔좻믱뗃뇪뗄,떫쯹횧뢶뗄볛룱늻쫇쯻뗄놨볛,뛸쫇쯹폐놨볛훐듎룟뗄튻룶(벴쯹캽뗚뛾볛룱)ꆣVickrey(1961)뗄뺭뗤럖컶뇭쏷,헢룶쪱뫲,싲랽틔ퟔ벺뗄맀볛춶뇪쫇폅뎬닟싔,튲벴뻹뫢닟싔ꆣ퓚헢훖뻹뫢닟싔쿂,ퟮ룟맀볛헟믱뗃뇪뗄뗄볛룱쫇듎룟춶뇪볛룱,튲뻍쫇듎룟맀볛,웤뷡맻뫍펢쪽엄싴쿠춬ꆣ퇐뺿뇭쏷,퓚룼튻냣뗄쳵볾쿂,샠쯆뗄뷡싛튲틀좻돉솢,펢쪽엄싴뫍뗚뛾볛룱쏜럢춶뇪튻냣돆쫇횧뢶뗈볛뗄,튲뻍쫇쮵웤쪵쿖뗄뷡맻쫇쿠춬뗄,떫죵폚뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪횮볤뗄닟싔뗈볛탔ꆣ듓틔짏뿉틔뾴떽,쯄훖엄싴춶뇪믺훆뛔폚싴랽살쮵웚췻쫕틦쫇쿠춬뗄ꆣ뛔폚룼튻냣뗄쟩뿶,퇐뺿컄쿗룸돶쇋춬퇹뷡맻,돆쫕틦뗈볛뚨샭,쯼쮵쏷:횻튪볙짨쳵볾쪹뗃ퟮ뫳뷡맻쫇맀볛ퟮ룟뗄죋믱뗃뇪뗄,뛸쟒뻟폐ퟮ뗍뿉쓜놣쇴볛룱뗄싲랽퓚엄싴춶뇪훐믱뗃뗄웚췻쫕틦캪0,쓇쎴쯄훖믺훆훐싴랽뗄웚췻쫕틦쫇튻퇹뗄ꆣ튲뻍쫇쮵듓웚췻쫕틦뗄뷇뛈뛸퇔,퓚쿠떱맣랺뗄쟩뿶쿂쯄훖엄싴믺훆뚼쫇뗈킧뗄ꆣ컒쏇쿖퓚뾼싇싴랽쫇럱쓜닉좡닟싔뛔엄싴춶뇪볓틔룉죅,듓뛸쪹뗃ퟔ벺뗄웚췻쫕틦뗃떽쳡룟ꆣ볙짨싴랽횸엉튻룶듺샭죋캱ힰ캪싲랽,돆캪뻖훐죋A,쯻뗄샻틦뫍싴랽췪좫튻훂ꆣ컒쏇뾼싇솽훖탅쾢짨뚨:튻훖쫇웤쯻싲랽늻쓜뇦뇰헢룶듺샭죋뗄짭럝,죏캪쯻튲쫇뫍ퟔ벺튻퇹뗄싲랽,튲뻍쫇쮵,쯻쏇죏캪닎폫엄싴춶뇪뗄늻쫇n죋,뛸쫇n+1죋ꆣ뗚뛾훖쫇웤쯻싲랽횪뗀(믲헟쮵닂떽)듺샭죋뗄헦쪵짭럝ꆣ뛔폚싴랽듺샭죋뿉틔닉폃뗄닟싔,컒쏇럖캪솽훖,튻훖쫇엔맛닟싔,튲뻍쫇쮵횻쫇놻뚯뗘닎폫엄싴춶뇪,뛸늻닉좡쪵훊탔뗄탐뚯ꆣ뛔폚싴랽살쮵,헢훖닟싔뇈뷏죝틗쪹폃,퓚엄싴훐횻튪맍벸룶죋뇭쿖돶ꆰ얨뫱ꆱ뗄릺싲탋좤,떫폖늻쪵볊닎폫돶볛벴뿉,퓚춶뇪훐싩랳튻킩,싴랽튲뿉틔뒮춨벸룶풭놾쎻폐탋좤닎폫춶뇪뗄싲랽,죃쯻쏇틔ퟮ뗍뿉쓜(늻뿉쓜훐뇪)뗄볛룱춶뇪,헢퇹쎻폐죎뫎럧쿕,좴쓜죃웤쯻싲랽닺짺듭컳뗄에뛏ꆣ싴랽듺샭죋뿉틔닉폃뗄뗚뛾훖닟싔쫇훷뚯닟싔,튲뻍쫇퓚엄싴춶뇪훐훷뚯돶볛(믲춶뇪),닎폫뺺헹,샻폃ퟔ벺뗄탐뚯살룉죅싲랽뗄뺺볛맽돌믲쮼캬ꆣ컒쏇헫뛔솽훖탅쾢짨뚨살럖뇰뾼달헢솽훖닟싔뗄킧맻ꆣ뛾ꆢ싲랽늻쓜뇦뇰듺샭죋짭럝뗄쒣탍싲랽늻횪뗀싴랽듺샭죋쫇뫍ퟔ벺늻춬뗄,틲듋헢믡퓬돉쯻쏇닟싔톡퓱짏뗄닮틬ꆣ1.펢쪽엄싴퓚펢쪽엄싴훐,싲랽뗄샭탔톡퓱쿔좻죔좻쫇:죧맻떱잰돶볛살ퟔ웤쯻뻖훐죋쟒뗍폚ퟔ벺뗄놣쇴볛룱,쓇쎴뻍돶룼룟뗄볛룱ꆣ퓚헢훖쟩뿶쿂,죧맻뻖훐죋A닉폃엔맛닟싔,퓲쯻늻믡뛔엄싴맽돌닺짺죎뫎펰쿬,늩?뷡뻖늻믡룄뇤,죔좻쫇뻟폐ퟮ룟vi뗄싲랽믱뗃뇪뗄,볛룱쫇듎룟뗄vi,싴랽뗄웚췻쫕틦캪(n-1)Π(n+1)ꆣ91
믆ꆡ쳎:엄싴춶뇪훐뗄싴랽룉죅닟싔럖컶죧맻뻖훐죋A닉좡훷뚯닟싔,쯻뇘탫뻶뚨쏦뛔뫎훖볛룱쪱돶룼룟뗄볛,퓚뫎훖볛룱쿂춣횹뺺볛ꆣ헢샯듦퓚솽훖뾼싇,죧맻쯻늻닎폫뺺볛,뿉쓜뻍쎻죋닎폫뺺볛쇋,뻍믡춣횹퓚떱잰볛룱,쯰쪧쇋뷸튻늽쳡볛뗄믺믡ꆣ죧맻쯻닎폫뺺볛,튲탭웤쯻싲랽믡늻퓙뺺헹,ퟔ벺믱뗃뇪뗄,헢쿠떱폚쇷뇪,뛔폚싴랽살쮵뻍쯰쪧쇋헢듎붫뇪뗄헦헽싴돶뗄믺믡ꆣ컒쏇볙짨돽쇋헢튻믺믡쯰쪧췢,쇷뇪뛔폚싴랽쎻폐쯰쪧ꆣퟷ캪샭싛짏뗄뾼달,컒쏇볙짨돶볛뿉틔죎틢캢킡뗘퓶볓ꆣ캪쇋떼돶뻖훐죋A뗄ퟮ폅닟싔,컒쏇뾼싇쯻퓚떱잰볛룱캪t쪱춣횹볌탸돶볛쪱뗄웚췻킧폃,헢튻볛룱믲헟살ퟔ쯻ퟔ벺,믲헟살ퟔ웤쯻싲랽ꆣ헢튻킧폃볇캪u(t:p1,ꆭ,pn),웤훐p1,ꆭ,pn쫇n룶싲랽틔췹쯹돶맽뗄ퟮ룟볛룱(죧맻쎻폐돶맽볛퓲캪0),뻖훐죋A펦룃룹뻝헢킩탅쾢탞헽뛔웤쯻싲랽헦쪵맀볛뗄탅쓮에뛏ꆣퟮ폅춣횹볛룱t탨튪싺ퟣuꇤ=0,듓쫽톧짏살쮵,헢튪쟳u(t+ꛅ)-u(t)뗄첩샕햹뾪훐ꛅ뗄쾵쫽캪0ꆣ컒쏇쿖퓚뾼달붫춣횹볛룱평t뇤떽t+ꛅ쪱싴랽쫕틦뗄뇤뮯(웤훐ꛅ>0),헢럖캪벸훖쟩뿶:(1)죧맻쯹폐뗄vi<t,퓲춣횹볛룱컞싛쫇t뮹쫇t+ꛅ,웤쯻싲랽뚼늻믡퓙닎폫뺺볛,틲듋싴랽쫕틦늻뇤,뚼쫇0;(2)훁짙솽룶싲랽뻟폐viꇝt+ꛅ,춣횹볛룱컞싛쫇t뮹쫇t+ꛅ,뚼늻믡룄뇤맀볛룟폚t+ꛅ뗄싲랽뗄뷸튻늽뺺볛,틲듋싴랽쫕틦늻뇤;(3)죧맻횻폐튻룶싲랽뻟폐vi>t+ꛅ뛸웤쯻싲랽뻟폐viꇜt,쓇쎴A돶볛t+ꛅ뫳돽쇋맀볛룟폚쯼뗄싲랽췢쎻폐웤쯻싲랽뺺볛,ퟮ뫳쫛볛붫쫇t+ꛅ,뛸죧맻닉폃춣횹볛룱tퟮ뫳쫛볛붫쫇t,쯹틔헢훖쟩뿶쿂싴랽쫕틦붫퓶볓ꛅ;(4)죧맻횻폐튻룶싲랽뻟폐viꇊ(t,t+ꛅ)뛸웤쯻싲랽뻟폐viꇜt,쓇쎴춣횹볛룱캪t쪱쫛볛캪t,춣횹볛룱캪t+ꛅ쪱쎻폐싲랽믡뷓쫜헢룶볛룱,뇪뗄실퓚듺샭죋쫖훐,쪵볊쫛볛캪0,쯹틔헢훖쟩뿶쿂싴랽쫕틦붫복짙tꆣ(5)웤쯻룷훖쟩뿶,퓚웤쯻룷훖쟩뿶쿂,튪쎴룅싊캪0(샽죧쒳룶싲랽맀볛헽뫃캪t),튪쎴뻟폐룟폚1뗄ꛅ뷗쫽(샽죧솽룶싲랽맀볛캪viꇊ(t,t+ꛅ),랢짺룅싊뗄ꛅ뷗쫽훁짙캪2),틲듋컒쏇뿉틔뫶싔헢킩쟩뿶ꆣퟛ짏쯹쫶,컒쏇횪뗀퓚u(t+ꛅ)-u(t)뗄첩샕햹뾪훐ꛅ뗄튻뷗뷼쯆캪(룟뷗쿮놻쪡싔):nnnnnn(1-t)ꛅꛅꇆꇇ(t-p)iꇆꇇ(t-p)(iꇆꇇt-p)ij=1i=1,iꇙjj=1i=1,iꇙjj=1i=1,iꇙj=n-tn=ꛅ(1-2t)nꇇ(1-p)iꇇ(1-p)iꇇ(1-p)ii=1i=1i=1(1)웤훐,쎿룶싲랽뗄뫳퇩룅싊럖늼캪:쟸볤[p)i,1]짏뗄뻹퓈럖늼,쏜뛈몯쫽캪1Π(1-pi,풭틲쫇,볈좻쯻틑돶볛pi,헢뻍틢캶ퟅ쯻뗄맀볛늻믡뗍폚piꆣ튪쟳(1)뗈폚0,뻍틢캶t=1Π2ퟅ,튲뻍쫇쮵,뛔폚뻖훐죋A뛸퇔,죧맻떱잰돶볛뗍폚1Π2,쯻뻍펦닎폫뺺볛,죧맻늻뗍폚1Π2,쯻뻍늻퓙닎폫ꆣ틲듋컒쏇폐뚨샭1:퓚펢쪽엄싴훐,죧맻싲랽늻쓜뇦뇰싴랽듺샭죋뗄짭럝,퓲엔맛닟싔뛔뷡맻쎻폐펰쿬,싴랽웚췻쫕틦죔좻쫇(n-1)Π(n+1),뛸ퟮ폅뗄훷뚯닟싔쫇틔맀볛캪1Π2뗄싲랽뗄랽쪽닎폫뺺볛,싴랽웚췻쫕틦캪:n11u=n1-+22ꇒ1n-2n-11n(n-1)(1-v)vvdv=+(2)1n+1n22(n+1)ꆡꆡ헢튻웚췻쫕틦럖캪솽늿럖,튻늿럖쫇횻폐튻룶싲랽맀볛룟폚1Π2뛸웤쯻싲랽맀볛뗍폚1Π2쪱뷡뻖캪틔1Π2돉붻쪱뗄쫕틦,쇭튻늿럖쫇폐솽룶믲틔짏싲랽맀볛룟폚1Π2쪱틔룟폚1Π2뗄듎룟볛룱쫛돶뇪뗄뗄쫕틦ꆣ훁폚쎻폐싲랽맀볛룟폚1Π2뗄쟩뿶,쫕틦캪0,퓚웚췻쫕틦릫쪽훐쎻폐뇭쿖ꆣ듓(2)컒쏇뿉틔뾴떽,퓚헢훖쟩뿶쿂,싴랽뿉틔춨맽듺샭죋훷뚯뺺볛살쒱쟳룼룟뗄웚췻쫕틦,떫92
2005쓪뗚7웚늻쓜춨맽듺샭죋뗄볲떥쿖짭뛸믱뗃뛮췢쫕틦ꆣ떱좻훷뚯뺺볛쫇폐럧쿕뗄,폐튻뚨뿉쓜쯹폐싲랽맀볛뚼뗍폚1Π2,룅싊캪n1Π2,헢룶쪱뫲훷뚯뺺볛뗄뷡맻쫇늻쓜쫛돶뇪뗄,쯰쪧쇋돶쫛믺믡ꆣ평듋뮹뿉틔뾴떽,헢훖쟩탎늻쫇엁샛췐ퟮ폅뗄,퓚풭놾뿉틔듯돉솽랽뻹폐샻뿉춼뗄붻틗쪱,평폚싴랽뗄닟싔탔뿘훆뛸즥쪧쇋헢튻믺믡ꆣ2.뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪평폚뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪훐뛔폚싲랽뛸퇔쫇닟싔탔뗈볛뗄,틲듋컒쏇튻늢볓틔뾼싇ꆣ퓚헢솽훖믺훆훐,싴랽듺샭죋닉좡훷뚯닟싔쫇쎻폐틢틥뗄,퓚뫉삼엄싴훐,횻튪싴랽듺샭죋튻떩뇭쪾뷓쫜떱잰뮹쎻폐놻싲랽뷓쫜뗄볛룱,뇪뗄뻍쫴쯻쯹폐,쯰쪧쇋헦헽뗄붻틗믺믡ꆣ뛸튻떩폐싲랽뷓쫜쇋떱잰볛룱,싴랽듺샭죋뻍쎻폐탐뚯뗄믺믡쇋ꆣ퓚뗚튻볛룱쏜럢춶뇪훐튲쿠샠쯆,죧맻돶볛뗍폚싲랽볛룱,쎻폐틢틥,죧맻룟폚싲랽볛룱,퓲믡쯰쪧붻틗믺믡ꆣ죧맻싲랽늻쓜뇦뇰싴랽듺샭죋뗄헦쪵짭럝,퓲싴랽듺샭죋뗄엔맛닟싔뻍ퟣ틔룄뇤싲랽뗄탐캪쇋ꆣ평폚헢룶쪱뫲,싲랽틔캪ퟜ릲폐n+1룶닎폫엄싴춶뇪뗄죋,틲듋쯻뗄볛룱닟싔붫믡쫇nviꆣn+1헢퇹ퟮ뫳믱뗃뇪뗄뗄죋쫇맀볛ퟮ룟뗄싲랽,평폚ퟮ룟맀볛뗄웚췻캪n,쯹틔싴랽웚췻쫕틦캪n+12nꆣn+1뚨샭2:퓚뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪훐,쎻폐훷뚯뺺볛닟싔뗄뿕볤,떫엔맛닟싔뻍ퟣ틔룄2뇤싴랽웚췻쫕틦,쪹웤뇤캪nꆣn+1폐좤뗄쫇,퓚싲랽늻쓜뇦뇰뗄쟩뿶쿂,횻튪n>1,퓚뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪훐,싴랽듺샭죋쪲쎴튲늻ퟶ뻍쓜쪹싴랽뗃떽뇈펢쪽엄싴훐닉좡훷뚯뺺볛닟싔룼룟뗄웚췻쫕틦ꆣ3.뗚뛾볛룱쏜럢춶뇪퓚뗚뛾볛룱쏜럢춶뇪훐,싲랽믡틔viퟷ캪춶뇪볛룱(Vickrey1961)ꆣ죧맻헢룶쪱뫲뻖훐죋A닉좡엔맛닟싔,퓲늻믡뛔뷡뻖닺짺죎뫎펰쿬ꆣ죧맻뻖훐죋A닉좡훷뚯닟싔,튲뻍쫇틔볛룱t춶뇪,쓇쎴싴랽뗄웚췻쫕틦캪:u=nn(1-t)t+ꇒ1n-2n(n-1)(1-v)vvdvn-12n=+nn+1t-t(3)n+1n+1ꆡꆡ튻뷗쳵볾뗃떽:n-1nnt-2nt=0(4)ꆡꆡퟮ폅뗄t캪1Π2,뫍펢쪽엄싴튻퇹ꆣ뚨샭3:퓚뗚뛾볛룱쏜럢춶뇪훐,싲랽늻쓜뇦뇰뗄쟩뿶쿂,싴랽듺샭죋뗄ퟮ폅닟싔뫍싴랽웚췻쫕틦뫍펢쪽엄싴튻퇹,튲뻍쫇엔맛닟싔컞킧,ퟮ폅훷뚯닟싔캪놣쇴볛룱1Π2,웚췻쫕틦튲쫇(2)ꆣ듓틔짏죽룶뚨샭살뾴,퓚싲랽늻쓜뇦뇰싴랽듺샭죋짭럝뗄쟩뿶쿂,쫕틦뗈볛뚨샭뗄뷡싛늻퓙돉솢ꆣ춬쪱,엔맛닟싔뛔펢쪽엄싴뫍뗚뛾볛룱쏜럢춶뇪컞킧,떫뛔뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪폐킧,훷뚯닟싔뛔펢쪽엄싴뫍뗚뛾볛룱쏜럢춶뇪폐킧,떫뛔뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪컞틢틥ꆣ죽ꆢ싲랽쓜릻뇦뇰싴랽듺샭죋뗄쒣탍죧맻싲랽쓜릻좷쟐뗘뇦뇰싴랽듺샭죋뗄헦쪵짭럝,튲뻍쫇쮵,횪뗀쯻늻맽쫇싴랽뗄ꆰ췐ꆱ,뷡맻믡퓵쎴퇹쓘?93
믆ꆡ쳎:엄싴춶뇪훐뗄싴랽룉죅닟싔럖컶쫗쿈,엔맛닟싔쿔좻뛔쯹폐쯄훖믺훆뚼컞킧,죧맻틑뺭횪뗀A늻쫇헦헽뗄싲랽,쓇쎴퓚뾼싇ퟔ벺뗄닟싔쪱쿔좻늻믡붫웤볆쯣퓚쓚ꆣ웤듎,벴뇣횪뗀싴랽듺샭죋뗄짭럝,퓚펢쪽엄싴뫍뗚뛾볛룱쏜럢춶뇪훐,훷뚯닟싔뗄킧맻죔좻돉솢ꆣ풭틲뫜볲떥,퓚펢쪽엄싴훐,쯤좻횪뗀쇋A뗄짭럝,떫죧맻쓣뗄맀볛뎬맽A떱잰룸돶뗄돶볛쪱,쓇쎴쓣쫇럱펦룃볓볛쓘?쿔좻죔좻펦룃볓볛ꆣ퓚뗚뛾볛룱쏜럢춶뇪훐,틔ퟔ벺뗄맀볛춶뇪죔좻쫇폅뎬닟싔,돶볛뻍폐믺믡믱뗃뇪뗄,늻돶볛쪲쎴믺믡뚼쎻폐쇋ꆣ틲듋횪뗀헢튻탅쾢늢늻믡룄뇤싲랽뗄돶볛닟싔,틲듋틔짏럖컶맽돌뫍뷡맻죔좻돉솢ꆣ떱좻,싴랽닙ퟝ퓚뗀뗂뫍램싉짏믡폶떽싩랳,횪뗀헢튻탅쾢퓚쿖쪵훐믡퓬돉늻춬,좻뛸늩?쒣탍쫇늻짦벰뗚죽랽믺훆뗄뒿듢닟싔뾼솿,틲듋웤럖컶뷡맻뻍쫇죧듋ꆣ죧맻럅떽쿖쪵뮷뺳훐럖컶싴랽닙ퟝ,뻍뿉틔쮵,헢샯뗄늩?쒣탍뇭쿖쇋닙ퟝ엄싴춶뇪뗄샻틦,헦쪵뗄싴랽뻍탨튪붫웤뫍쪹폃닟싔뗄뗀뗂믲램싉럧쿕쿠좨뫢쇋ꆣ뛔폚뫉삼엄싴뫍뗚튻볛룱엄싴살쮵,쟩뿶폐쯹늻춬ꆣ쿖퓚싲랽횪뗀쇋ퟔ벺뇘탫뫍튻룶싴랽듺샭죋뺺볛,웤뷡맻믡죧뫎쓘?퓚쿖퓚뗄닟싔탍늩?훐,뻖훐죋A튪톡퓱돶볛t,뻖훐죋i튪톡퓱돶볛pi,쯼쫇웤맀볛뗄몯쫽ꆣ뾼달싲랽뗄뛔돆뻹뫢닟싔,튲뻍쫇닉폃춬퇹뗄뚨볛몯쫽pi=f(v)iꆣ캪쇋믱뗃뻹뫢닟싔,컒쏇쫗쿈뾼싇싲랽뛔뻖훐죋A뗄닟싔t폫웤쯻싲랽뗄닟싔뗄ퟮ폅랴펦ꆣ쿔좻,죧맻vi<t,쓇쎴죎뫎piꇊ[0,t]뚼늻쓜믱뗃뇪뗄,튲뚼쫇ퟮ폅랴펦,죧맻viꇝt,퓲펦룃닉좡pi=f(v)iꇝtꆣ짨f(ꆤ)뗄랴몯쫽캪g(ꆤ),퓲뻖훐죋i뗄웚췻킧폃캪:n-1ui=[g(p)i](vi-p)iꆡ뛔폚ꆡviꇝt(5)ꆡꆡ룹뻝튻뷗쳵볾,컒쏇뗃떽:(n-1)(v)i-pigꇤ-g(p)i=0(6)ꆡꆡ룹뻝볙짨,pi=f(v)i싺ퟣ(6)뫍gꇤ(p)i=1Πfꇤ(v)iꆣ뚨틥hꇔfΠvi,듸죫뫳폐vihꇤ=(n-1)-nh(7)ꆡꆡ헢튻랽돌뻟폐튻룶죃죋쫬쾤뗄뷢n-1:f=hvi=vni,튲뻍쫇Vickrey믹놾쒣탍훐뗄ퟮ폅닟싔ꆣ퓚헢샯컒쏇룐탋좤뗄쫇싺ퟣf(t)=t뗄뷢,헢룶뷢닅쫇컒쏇짨뚨쿂뗄ퟮ폅랴펦몯쫽,웤뷡맻쫇n-11pi=f(v)i=hvi=+n(tΠv)iv(i8)nnꆡꆡ쿖퓚컒쏇뾼달뻖훐죋A뛔폚싲랽쪹폃닟싔뗄ퟮ폅랴펦ꆣ쿔좻,죧맻싲랽뗄닟싔훐,뛔폚쯹폐vi>0뚼짨뚨pi>0,쓇쎴뻖훐죋Aퟮ폅뗄t믡쫇0,풭틲쫇t>0횻믡떼훂믺믡쯰쪧(쯹폐pi<t쪱쯰쪧붻틗믺믡),늻듸살죎뫎쫕틦ꆣ죧맻싲랽뗄닟싔훐듦퓚쒳룶t0,싲랽퓚vi<t0쪱짨뚨pi=0,퓚viꇝt0쪱짨뚨piꇝt,쓇쎴톡퓱죎틢tꇊ[0,t0]뚼믡쫇뻖훐죋A쏦뛔헢훖싲랽닟싔뗄ퟮ폅랴펦ꆣ붫솽훖ퟮ폅랴펦솪솢웰살뾴컒쏇뿉틔뗃떽듳솿쓉쪲뻹뫢,뇭쿖퓚틔쿂뚨샭훐ꆣ뚨샭4:죧맻싲랽횪뗀싴랽듺샭죋뗄헦쪵짭럝,퓲엔맛닟싔뛔쯹폐쯄훖믺훆뚼쪧킧,뛸훷뚯닟싔뛔펢쪽엄싴뫍뗚뛾볛룱쏜럢춶뇪폐킧,뷡맻뫍늻쓜뇦뇰뗄쟩탎쿠춬ꆣ훷뚯닟싔뛔뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪폐킧,틔쿂닟싔ퟩ뫏뚼쫇쓉쪲뻹뫢:싴랽듺샭죋톡퓱tꇊ[0,1),싲랽i퓚vi<t쪱늻돶볛믲틔0춶뇪,퓚viꇝt쪱틔(8)훐뗄볛룱돶볛ꆣ퓚싲랽쓜뇦뇰싴랽듺샭죋짭럝쪱,쫕틦뗈볛뚨샭늻쓜놣횤돉솢,풭틲쫇퓚뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪훐듦퓚듳솿뻹뫢,뫜쓑쮵쓄튻룶뻍튻뚨퓚쿖쪵훐돶쿖,듺샭죋짨뚨t=0뛔펦폚믹놾쒣탍,듺샭죋짨뚨t=1Π2퓲폫펢쪽엄싴벰뗚뛾볛룱쏜럢춶뇪쿠춬,떫tꇊ[0,1)훐죎틢쫽횵뚼뿉틔릹돉쓉쪲뻹뫢,뻟쳥뫎헟쪵쿖튪뾴탎쫆훐뗄탄샭뫍뮷뺳틲쯘뗄펰쿬ꆣ94
2005쓪뗚7웚쯄ꆢ킡ꆡ뷡퓚쒣탍훐,엔맛닟싔뷶퓚싲랽늻횪뗀싴랽듺샭죋헦쪵짭럝쪱뛔뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪폐킧,평폚쯼틀삵폚탅쾢ힴ뿶,틲듋컒쏇뿉틔돆횮캪엄싴춶뇪뗄탅쾢룉죅ꆣ쪹폃헢훖닟싔뛔폚싴랽살쮵쫇ퟮ랽뇣뗄,횻튪뺡뿉쓜뛠뗘헐벯살싲랽믲쿱싲랽뗄죋벴뿉,램싉뫍뗀뗂짏뗄럧쿕튲뫜킡ꆣ듓ퟩ횯탎쪽살뾴,뫉삼엄싴쫇ퟮ죝틗쫜떽헢훖룉죅뗄,횻튪폐튻듳냯죋퓚뎡뮢쫓,맀볛ퟮ룟뗄싲랽뻍룼뿉쓜뷓쫜뇈쪵볊탨튪룼룟뗄볛룱ꆣ뛸펢쪽엄싴늻믡쫜탅쾢룉죅뗄펰쿬,헢뿖엂뻍쫇폫펢쪽엄싴쿠뇈,뫉삼엄싴퓚쿖쪵훐뫜짙닉폃뗄훘튪샭평횮튻(싲랽룼쾲뮶닎폫펢쪽엄싴)ꆣ훷뚯닟싔탨튪싴랽듺샭죋ퟶ돶쪵볊뗄돶볛뫍춶뇪탐뚯,컒쏇뿉틔돆횮캪탐뚯룉죅ꆣ닉폃헢훖닟싔뛔폚싴랽살쮵뻟폐튻뚨뗄럧쿕,뷶뻍늩?살쮵,뻍듦퓚뇪뗄실죫듺샭죋쫖훐헢튻컞틢틥붻틗뗄럧쿕,퓚늩?뷡릹횮췢뮹듦퓚뗀뗂뫍램싉럧쿕ꆣ좻뛸,퓚죵볠맜뗄짧믡훐,닉폃헢킩쫖뛎쫇폐뿉쓜뗄,쳘뇰쫇싴랽뮹뿉틔닉좡쒳킩뇤춨쫖뛎볓틔쪵쿖ꆣ샽죧,싴랽뿉틔뫍쒳룶싲랽듯돉릲쒱,싲랽틔싴랽듺샭죋짭럝탐뚯,첧룟볛룱,죧맻뇪뗄실죫릲쒱싲랽쫖훐,싴랽뷶튪쟳싲랽횧뢶뗍폚웤돶볛뗄볛룱ꆣ죧맻뇪뗄돉릦뗘틔뷏룟볛룱돶쫛룸웤쯻싲랽,퓲싴랽뛔릲쒱랽닉좡쒳훖탎쪽뗄늹뎥(짵훁뎤웚뫏ퟷ놾짭뻍뿉틔폕쪹쒳룶싲랽폫싴랽릲쒱)ꆣ탐뚯룉죅뛔폚펢쪽엄싴뫍뗚뛾볛룱쏜럢춶뇪ퟜ쫇폐킧뗄ꆣ뛔폚뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪뗄킧맻퓲쫜떽탅쾢짨뚨뗄펰쿬,폐좤뗄쫇,랢짺킧솦횻폐퓚싲랽횪뗀싴랽듺샭죋헦쪵짭럝뗄쪱뫲,뛸쟒킧맻튲뇭쿖캪듳솿뗄쓉쪲뻹뫢춬쪱듦퓚,뫜쓑풤퇔뫎헟튻뚨믡돶쿖,헢믡퓶볓싴랽쪹폃헢튻닟싔뗄쓑뛈,틲듋컒쏇뿉틔쮵뫉삼엄싴뫍뗚튻볛룱쏜럢춶뇪뛔폚탐뚯룉죅뻟폐튻뚨럀횹탔ꆣ듓쳖싛훐컒쏇뿉틔뾴떽,싴랽뗄늻춬룉죅뛔폚늻춬믺훆킧맻쫇늻튻퇹뗄,쫕틦뗈볛뚨샭쯹뇭쿖뗄믺훆뗈킧탔늻퓙듦퓚,헢뻍쳡릩쇋퓚쿖쪵믺훆톡퓱쪱뿉틔닎뾼뗄튻훖놳뺰쮼슷,탨튪룹뻝탅쾢룉죅뫍탐뚯룉죅뗄쪵쪩쓑틗돌뛈뫍킧맻살뷸탐믺훆뗄짨볆뫍횴탐ꆣ닎뾼컄쿗Bulow,,.,1989,ꆰTheSimpleEconomicsofOptimalAuctionsꆱ,JournalofPoliticalEconomy,97,1060ꆪ,.,andMarshall,.,1987,ꆰCollusiveBidderBehaviorataSingleObjectSecondPriceandEnglishAuctionꆱ,JournalofPoliticalEconomy,95,1217ꆪ,.,andRiley,.,2000,ꆰExistenceofEquilibriuminSealedHighBidAuctionsꆱ,ReviewofEconomicStudies,,,J.,1992,ꆰBiddingRingsꆱ,AmericanEconomicReview,82,579ꆪ,P.,1981,ꆰRationalExpectations,InformationAcquisitionandCompetitiveBiddingꆱ,Econometrica,49,921ꆪ,.,1981,ꆰOptimalAuctionDesignꆱ,MathematicsofOperationsResearch,6,58ꆪ,.,andSamuelson,.,1981,ꆰOptimalAuctionsꆱ,AmericanEconomicReview,71,381ꆪ,W.,1961,ꆰCounterspeculation,Auctions,andCompetitiveSealedTendersꆱ,JournalofFinance,16,8ꆪ(GuanghuaSchoolofManagement,PekingUniversity)Abstract:Inthispaper,::Auction;Game;StrategyJELClassification:C720(퓰죎뇠벭:폡퇇샶)(킣뛔:쿾ꆡ언)95
