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-TongChau7FulbrightGuestLectureMaterialsCanPrivateInformationtoAgentBenefitthePrincipal?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)071.51000n/a10,173.5Summaryofresults: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-TongChau18FulbrightGuestLectureMaterialsInConclusion,Wecannotguarranteethatpeoplewillalwaysdotheethicallycorrectthings.Therefore,theywillhavetobemonitoredandcontrolled.Informationsystemsprovideuswiththemeansto:informuswhathashappened,andmotivatepeopletodotheethicallycorrectthings.Itisthereforeimportanttoconsiderthesepointsindesigninganymanagerialaccountingsystems.Dr.Chak-TongChau19FulbrightGuestLectureMaterials9、靜夜夜四無無鄰，，荒居居舊業(yè)業(yè)貧。。。1月-231月-23Friday,January6,202310、雨中黃葉葉樹，燈下下白頭人。。。01:08:4701:08:4701:081/6/20231:08:47AM11、以我獨沈久久，愧君相見見頻。。1月-2301:08:4701:08Jan-2306-Jan-2312、故人人江海海別，，幾度度隔山山川。。。01:08:4701:08:4701:08Friday,January6,202313、乍見翻翻疑夢，，相悲各各問年。。。1月-231月-2301:08:4701:08:47January6,202314、他鄉(xiāng)鄉(xiāng)生白白發(fā)，，舊國國見青青山。。。06一一月月20231:08:47上上午01:08:471月-2315、比比不不了了得得就就不不比比，，得得不不到到的的就就不不要要。。。。。一月月231:08上上午午1月月-2301:08January6,202316、行動出出成果，，工作出出財富。。。2023/1/61:08:4701:08:4706January202317、做前，，能夠環(huán)環(huán)視四周周；做時時，你只只能或者者最好沿沿著以腳腳為起點點的射線線向前。。。1:08:47上午午1:08上午午01:08:471月-239、沒有失敗敗，只有暫暫時停止成成功！。1月-231月-23Friday,January6,202310、很多事情努努力了未必有有結(jié)果，但是是不努力卻什什么改變也沒沒有。。01:08:4701:08:4701:081/6/20231:08:47AM11、成成功功就就是是日日復復一一日日那那一一點點點點小小小小努努力力的的積積累累。。。。1月月-2301:08:4701:08Jan-2306-Jan-2312、世間成事，，不求其絕對對圓滿，留一一份不足，可可得無限完美美。。01:08:4701:08:4701:08Friday,January6,202313、不知香積積寺，數(shù)里里入云峰。。。1月-231月-2301:08:4701:08:47January6,202314、意志堅強的的人能把世界界放在手中像像泥塊一樣任任意揉捏。06一月20231:08:47上午01:08:471月-2315、楚塞三三湘接，，荊門九九派