精選數(shù)據(jù)系統(tǒng)和主要的代理模式

InformationSystemsunderPrincipal-agentModeling

Dr.Chak-TongChau

仇澤棠博士U.S.FulbrightProfessor中美交流富布萊特教授WhatIsInformation?

Broadlydefined,informationisanydevicethathelpstoreduceuncertainty. Alternatively,informationshouldbehelpfulin:detectingthecurrentstateoftheworld,orforecastingthefuturestateoftheworldDr.Chak-TongChau2FulbrightGuestLectureMaterialsGoodInformationShouldbeUsefulin:Improvingproductiondecisions–tellingustodotherightthings.Optimizingthescopeforrisksharing–sothatsomepeoplecannotmakeprofitsbyharmingotherpeople.Eliminating“informationasymmetry”–sothatexante(before-the-act)privateinformationcanbeknownexpost(after-the-act).Dr.Chak-TongChau3FulbrightGuestLectureMaterialsTimelineofatypicalagencycontractContractagreedEffortselectedPayoffrevealedPre-contractinformationPre-effortselectioninformationPost-effortinformationPost-payoffinformationTimingInformationAvailabilityToagentonly(private)Toallparties(public)Pre-contractAgent’sproprietaryknowledgeHistoricalinformationPost-contract,pre-effortInformationsetunderdecentralizationPost-effort,pre-payoffVoluntarydisclosure–relevationprinciplePostpayoff(expost)NotinterestingFinancialreportingDr.Chak-TongChau4FulbrightGuestLectureMaterialsUsefulnessofInformationHowdoweknow,apriori,thatinformationis“useful”?Considerthefollowingpayoffstructure(knowntoall):EffortS1S2S3S4S5S6ExpectedPayoffe1=102334553.67e2=52234453.33Dr.Chak-TongChau5FulbrightGuestLectureMaterialsUsefulnessofInformationNow,wehaveaninformationsystemthatwillgeneratethesesignals:{S1,S2,S3}{S4,S5,S6}Y1Y2Signal:Y1Y2S1S2S3S4S5S6e1=10233455e2=5223445Inasense,theinformationsystempartitionsthematrixasfollowsQuestion:Arethesignals,Y1andY2,useful?Dr.Chak-TongChau6FulbrightGuestLectureMaterialsUsefulnessofInformationNow,wehaveanotherinformationsystemthatwillgeneratethesesignals:{S1}{S4,S5,S6}Y1Y3Signal:Y1Y2Y3S1S2S3S4S5S6e1=10233455e2=5223445ThisnewinformationsystempartitionsthematrixasfollowsQuestion:Arethesignals,Y1,,Y2andY3useful?{S2,S3}Y2Dr.Chak-TongChau7FulbrightGuestLectureMaterialsExpectedPayofftoPChak-TongChauNow,ifthePrincipalcannotobserveeffort,howwouldhepaytheagent?Agent’sUtilityFunction:U=X?-e2100Principal’sPayoffsHistoricalinformationCanPrivateInformationtoAgentBenefitthePrincipal?Question:Arethesignals,Y1,,Y2andY3useful?UsefulnessofInformationFixedsalary,effortunobservableExpectedPayofftoPrincipalbeforePaymenttoAgentUsefulnessofInformation十月224:36下午10月-2216:36October30,20225–62=102.ThisnewinformationsystempartitionsthematrixasfollowsFulbrightGuestLectureMaterialsCanPrivateInformationtoAgentBenefitthePrincipal?Considerthefollowingpayoffstructure(knowntoall):S1S2S3S4ExpectedPayofftoPrincipalbeforePaymenttoAgentProb.50.25e1=000000e2=520,00020,00025,00030,00023,750e2=620,00030,00030,00035,00028,750Agent’sUtilityFunction:

U=X?-e2

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

=18,496Dr.Chak-TongChau8FulbrightGuestLectureMaterialsCanPrivateInformationtoAgentBenefitthePrincipal?Now,ifthePrincipalcannotobserveeffort,howwouldhepaytheagent?Howaboutthiscompensationcontract(afixedsalaryof$18,496)toagent?Wouldthiswork?S1S2S3S4ExpectedUtilitytoAExpectedPayofftoPProb.50.25e1=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-TongChau9FulbrightGuestLectureMaterialsCanPrivateInformationtoAgentBenefitthePrincipal?Nowthen,whataboutacontingentsalaryof$18,496toagent?WouldthisimprovethePrincipal’spayoff?S1S2S3S4ExpectedUtilitytoAExpectedPayofftoPProb.50.25e1=00000e2=518,49618,496018,496e3=618,49618,49618,49618,496

07710009,878

10,254Now,thecontingentsalarycontractwillimprovebyforcingtheAgenttogive(e3=6).Letusnowlookatthe“privateinformationtoagent”issue!Dr.Chak-TongChau10FulbrightGuestLectureMaterialsCanPrivateInformationtoAgentBenefitthePrincipal?Thisprivateinformationsystem(onlyobservabletotheagent)generatesthesesignals:{S1,S2}{S3,S4}Y1Y2Wouldthecontingentsalaryof$18,496toagentstillwork?Signal:Y1Y2ExpectedUtilitytoAgentwithPrivateinfoExpectedPayofftoPrincipalwithPrivateinfoS1S2S3S4Prob.50.25e1=00000e2=518,49618,496018,496105.5(100)7,754(10,254)e3=618,49618,49618,49618,496Dr.Chak-TongChau11FulbrightGuestLectureMaterialsCanPrivateInformationtoAgentBenefitthePrincipal?Now,thenewprivateinformationmakesiteasyfortheagenttocheat.So,whatshouldtheprincipaldo?Considerthisnewcontingentcontract(correspondingpayoffs):S1S2S3S4Prob.50.25e1=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-TongChau12FulbrightGuestLectureMaterialsS1S2S3S4ExpectedUtilitytoAExpectedPayofftoPProb.50.25e1=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-TongChau13FulbrightGuestLectureMaterialsPre-effort“Public”Information?Thistime,itisdifferentinthattheinformationisavailabletoall,principalandagent.(changed)S1S2S3S4Prob.50.25e1=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-TongChau14FulbrightGuestLectureMaterialsSignal:Y1Y2ExpectedUtilitytoAgentExpectedPayofftoPrincipalS1S2S3S4Prob.50.25e1=00000e2=518,4960018,49610010,254e3=618,49618,49618,49618,496First,theinformationhasnovaluetotheagent.Why?Thisisbecausetheagent,byobservingY1,cannotguarranteethatthepayoff$25,000willnotoccur.However,isthiskindofinformationsystemusefultothePrincipal?Dr.Chak-TongChau15FulbrightGuestLectureMaterialsNow,letuslookatthisnewcontract(correspondingpayoffs):Signal:Y1Y2S1S2S3S4Prob.50.25e1=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-TongChau16FulbrightGuestLectureMaterialsSignal:Y1Y2S1S2S3S4Prob.50.25e1=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-TongChau17FulbrightGuestLectureMaterialsButforthePrincipal,whyshouldhecare?Signal:Y1Y2S1S2S3S4Prob.50.25e2=520,00025,000

e3=630,00035,000WagestoA(15,170)(15,170)(17,030)(21,074)ExpectedResidual1,207.502,457.503,242.503,481.5010,389Notethatthisislargerthan10,254,theoptimalsolutionunderperfectinformation.Thus,seeminglyuselessinformationcanbeuseful!Dr.Chak-TongChau18FulbrightGuestLectureMaterialsMOMODAPOWERPOINT10月-2210月-2216:59:1916:59:19October30,2022{S4,S5,S6}勝人者有力，自勝者強(qiáng)。EffortselectedFinancialreportingChak-TongChauPostpayoff(expost)Fusceidurnablandit,eleifendnullaac,fringillapurus.Chak-TongChauFulbrightGuestLectureMaterials17、做前，能夠環(huán)視四周；UsefulnessofInformationChak-TongChauThispublicinformationsystem(observabletoall)generatesthesesignals:InConclusion,Wecannotguarranteethatpeoplewillalwaysdotheethicallycorrectthings.Therefore,theywillhavetobemonitoredandcontrolled.Informationsystemsprovideuswiththemeansto:informuswhathashappened,andmotivatepeopletodotheethicallycorrectthings.Itisthereforeimportanttoconsiderthesepointsindesigninganymanagerialaccountingsystems.Dr.Chak-TongChau19FulbrightGuestLectureMaterials9、靜夜四無(wú)鄰，荒居舊業(yè)貧。。12月-2212月-22Tuesday,December13,202210、雨中黃葉樹，燈下白頭人。。21:26:3621:26:3621:2612/13/20229:26:36PM11、以我獨(dú)沈久，愧君相見(jiàn)頻。。12月-2221:26:3621:26Dec-2213-Dec-2212、故人江海別，幾度隔山川。。21:26:3621:26:3621:26Tuesday,December13,202213、乍見(jiàn)翻疑夢(mèng)，相悲各問(wèn)年。。12月-2212月-2221:26:3621:26:36December13,202214、他鄉(xiāng)生白發(fā)，舊國(guó)見(jiàn)青山。。13十二月20229:26:36下午21:26:3612月-2215、比不了得就不比，得不到的就不要。。。十二月229:26下午12月-2221:26December13,202216、行動(dòng)出成果，工作出財(cái)富。。2022/12/1321:26:3621:26:3613December202217、做前，能夠環(huán)視四周；做時(shí)，你只能或者最好沿著以腳為起點(diǎn)的射線向前。。9:26:36下午9:26下午21:26:3612月-229、沒(méi)有失敗，只有暫時(shí)停止成功！。12月-2212月-22Tuesday,December13,202210、很多事情努力了未必有結(jié)果，但是不努力卻什么改變也沒(méi)有。。21:26:3621:26:3621:2612/13/20229:26:36PM11、成功就是日復(fù)一日那一點(diǎn)點(diǎn)小小努力的積累。。12月-2221:26:3621:2