数据系统和主要的代理模式概述

InformationSystemsunderPrincipal-agentModeling

Dr.Chak-TongChau

仇澤棠博士U.S.FulbrightProfessor中美交流富布萊特教授1数据系统和主要的代理模式概述第1页WhatIsInformation?

Broadlydefined,informationisanydevicethathelpstoreduceuncertainty. Alternatively,informationshouldbehelpfulin:detectingthecurrentstateoftheworld,orforecastingthefuturestateoftheworldDr.Chak-TongChau2FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第2页GoodInformationShouldbeUsefulin:Improvingproductiondecisions–tellingustodotherightthings.Optimizingthescopeforrisksharing–sothatsomepeoplecannotmakeprofitsbyharmingotherpeople.Eliminating“informationasymmetry”–sothatexante(before-the-act)privateinformationcanbeknownexpost(after-the-act).Dr.Chak-TongChau3FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第3页TimelineofatypicalagencycontractContractagreedEffortselectedPayoffrevealedPre-contractinformationPre-effortselectioninformationPost-effortinformationPost-payoffinformationTimingInformationAvailabilityToagentonly(private)Toallparties(public)Pre-contractAgent’sproprietaryknowledgeHistoricalinformationPost-contract,pre-effortInformationsetunderdecentralizationPost-effort,pre-payoffVoluntarydisclosure–relevationprinciplePostpayoff(expost)NotinterestingFinancialreportingDr.Chak-TongChau4FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第4页UsefulnessofInformationHowdoweknow,apriori,thatinformationis“useful”?Considerthefollowingpayoffstructure(knowntoall):EffortS1S2S3S4S5S6ExpectedPayoffe1=102334553.67e2=52234453.33Dr.Chak-TongChau5FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第5页UsefulnessofInformationNow,wehaveaninformationsystemthatwillgeneratethesesignals:{S1,S2,S3}{S4,S5,S6}Y1Y2Signal:Y1Y2S1S2S3S4S5S6e1=10233455e2=5223445Inasense,theinformationsystempartitionsthematrixasfollowsQuestion:Arethesignals,Y1andY2,useful?Dr.Chak-TongChau6FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第6页UsefulnessofInformationNow,wehaveanotherinformationsystemthatwillgeneratethesesignals:{S1}{S4,S5,S6}Y1Y3Signal:Y1Y2Y3S1S2S3S4S5S6e1=10233455e2=5223445ThisnewinformationsystempartitionsthematrixasfollowsQuestion:Arethesignals,Y1,,Y2andY3useful?{S2,S3}Y2Dr.Chak-TongChau7FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第7页CanPrivateInformationtoAgentBenefitthePrincipal?Considerthefollowingpayoffstructure(knowntoall):S1S2S3S4ExpectedPayofftoPrincipalbeforePaymenttoAgentProb.0.250.250.250.25e1=000000e2=520,00020,00025,00030,00023,750e2=620,00030,00030,00035,00028,750Agent’sUtilityFunction:

U=X½-e2

100where: X=agent’scompensations e=theeffortlevelusedbytheagentIfthePrincipalcanobserveeffort,howwouldhepaytheagent?X½-62=100X

=18,496Dr.Chak-TongChau8FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第8页CanPrivateInformationtoAgentBenefitthePrincipal?Now,ifthePrincipalcannotobserveeffort,howwouldhepaytheagent?Howaboutthiscompensationcontract(afixedsalaryof$18,496)toagent?Wouldthiswork?S1S2S3S4ExpectedUtilitytoAExpectedPayofftoPProb.0.250.250.250.25e1=018,49618,49618,49618,496e2=518,49618,49618,49618,496e3=618,49618,49618,49618,496136111100-18,4965,254

10,254Thus,afixedsalarytosomeonewhomyoucannotobservewon’twork.A“moralhazard”problemwillcomeintoplay.Dr.Chak-TongChau9FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第9页CanPrivateInformationtoAgentBenefitthePrincipal?Nowthen,whataboutacontingentsalaryof$18,496toagent?WouldthisimprovethePrincipal’spayoff?S1S2S3S4ExpectedUtilitytoAExpectedPayofftoPProb.0.250.250.250.25e1=00000e2=518,49618,496018,496e3=618,49618,49618,49618,496

07710009,878

10,254Now,thecontingentsalarycontractwillimprovebyforcingtheAgenttogive(e3=6).Letusnowlookatthe“privateinformationtoagent”issue!Dr.Chak-TongChau10FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第10页CanPrivateInformationtoAgentBenefitthePrincipal?Thisprivateinformationsystem(onlyobservabletotheagent)generatesthesesignals:{S1,S2}{S3,S4}Y1Y2Wouldthecontingentsalaryof$18,496toagentstillwork?Signal:Y1Y2ExpectedUtilitytoAgentwithPrivateinfoExpectedPayofftoPrincipalwithPrivateinfoS1S2S3S4Prob.0.250.250.250.25e1=00000e2=518,49618,496018,496105.5(100)7,754(10,254)e3=618,49618,49618,49618,496Dr.Chak-TongChau11FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第11页CanPrivateInformationtoAgentBenefitthePrincipal?Now,thenewprivateinformationmakesiteasyfortheagenttocheat.So,whatshouldtheprincipaldo?Considerthisnewcontingentcontract(correspondingpayoffs):S1S2S3S4Prob.0.250.250.250.25e1=00000e2=514,722(20,000)14,722(20,000)

0(25,000)20,544(30,000)e3=614,722(20,000)20,544(30,000)20,544(30,000)18,496(35,000)Wouldthenewplanwork?Letuscalculatetheagent’sutilityandtheprincipal’spayoff.Dr.Chak-TongChau12FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第12页S1S2S3S4ExpectedUtilitytoAExpectedPayofftoPProb.0.250.250.250.25e1=00000e2=514,722(20,000)14,722(20,000)

0(25,000)20,544(30,000)e3=614,722(20,000)20,544(30,000)20,544(30,000)18,496(35,000)

071.51000

n/a

10,173.5Summaryofresults:TypesofcontractPrincipal’sPayoffsAgent’sUtilityFixedsalary,effortobservable10,254100.0Fixedsalary,effortunobservable-18,496136.0Contingentsalary,noprivateinformation10,254100.0One-amount,withprivateinformation7,754105.5Multiple-amount,withprivateinformation10,173.5100.0Dr.Chak-TongChau13FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第13页Pre-effort“Public”Information?Thistime,itisdifferentinthattheinformationisavailabletoall,principalandagent.(changed)S1S2S3S4Prob.0.250.250.250.25e1=00000e2=520,000(18,496)25,000(0)25,000(0)30,000(18,496)e2=620,000(18,496)30,000(18,496)30,000(18,496)35,000(18,496)Thispublicinformationsystem(observabletoall)generatesthesesignals:{S1,S2}{S3,S4}Y1Y2Isthisinformationusefultotheagent?Dr.Chak-TongChau14FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第14页Signal:Y1Y2ExpectedUtilitytoAgentExpectedPayofftoPrincipalS1S2S3S4Prob.0.250.250.250.25e1=00000e2=518,4960018,49610010,254e3=618,49618,49618,49618,496First,theinformationhasnovaluetotheagent.Why?Thisisbecausetheagent,byobservingY1,cannotguarranteethatthepayoff$25,000willnotoccur.However,isthiskindofinformationsystemusefultothePrincipal?Dr.Chak-TongChau15FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第15页Now,letuslookatthisnewcontract(correspondingpayoffs):Signal:Y1Y2S1S2S3S4Prob.0.250.250.250.25e1=00000e2=515,170(20,000)15,170(25,000)

15,170(25,000)17,030(30,000)e3=615,170(20,000)17,030(30,000)17,030(30,000)21,074(35,000)Now,ifY1isobserved,whatwouldtheagentdo?U(e2)=15,1701/2–52=98.17U(e3)=15,1701/2*0.5+17,0301/2*0.5–62=90.89Thus,thePrincipalinfacttellstheagenttobelazy!Dr.Chak-TongChau16FulbrightGuestLectureMaterials数据系统和主要的代理模式概述第16页Signal:Y1Y2S1S2S3S4Prob.0.250.250.250.25e1=00000e2=515,170(20,000)15,170(25,000)

15,170(25,000)17,030(30,000)e3=615,170(20,000)17,030(30,000)17,030(30,000)21,074(35,000)Then,ifY2isobserved,whatwouldtheagentdo?U(e2)=15,1701/2*0.5+17,0301/2*0.5–52=101.88U(e3)=17,0301/2*0.5+21,0741/2*0.5–62=102.03Thistime,theagentwillwanttoworkhard.Onaverage,98.17*0.5+102.03*0.5=100So,thisisacceptabletotheagent.Dr.Chak-TongChau17FulbrightGuestLectureMaterials数据系统