Information Systems and Principal Agent Models

InformationSystemsunderPrincipal-agentModeling,Dr.Chak-TongChau仇澤棠博士U.S.FulbrightProfessor中美交流富布萊特教授,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,2,WhatIsInformation?,Broadlydefined,informationisanydevicethathelpstoreduceuncertainty.Alternatively,informationshouldbehelpfulin:detectingthecurrentstateoftheworld,orforecastingthefuturestateoftheworld,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,3,GoodInformationShouldbeUsefulin:,Improvingproductiondecisionstellingustodotherightthings.Optimizingthescopeforrisksharingsothatsomepeoplecannotmakeprofitsbyharmingotherpeople.Eliminating“informationasymmetry”sothatexante(before-the-act)privateinformationcanbeknownexpost(after-the-act).,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,4,Timelineofatypicalagencycontract,Contractagreed,Effortselected,Payoffrevealed,Pre-contractinformation,Pre-effortselectioninformation,Post-effortinformation,Post-payoffinformation,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,5,UsefulnessofInformation,Howdoweknow,apriori,thatinformationis“useful”?,Considerthefollowingpayoffstructure(knowntoall):,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,6,UsefulnessofInformation,Now,wehaveaninformationsystemthatwillgeneratethesesignals:,S1,S2,S3,S4,S5,S6,Y1,Y2,Inasense,theinformationsystempartitionsthematrixasfollows,Question:Arethesignals,Y1andY2,useful?,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,7,UsefulnessofInformation,Now,wehaveanotherinformationsystemthatwillgeneratethesesignals:,S1,S4,S5,S6,Y1,Y3,Thisnewinformationsystempartitionsthematrixasfollows,Question:Arethesignals,Y1,Y2andY3useful?,S2,S3,Y2,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,8,CanPrivateInformationtoAgentBenefitthePrincipal?,Considerthefollowingpayoffstructure(knowntoall):,AgentsUtilityFunction:U=X-e2100where:X=agentscompensationse=theeffortlevelusedbytheagent,IfthePrincipalcanobserveeffort,howwouldhepaytheagent?,X-62=100,X=18,496,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,9,CanPrivateInformationtoAgentBenefitthePrincipal?,Now,ifthePrincipalcannotobserveeffort,howwouldhepaytheagent?,136,111,100,-18,496,5,254,10,254,Thus,afixedsalarytosomeonewhomyoucannotobservewontwork.A“moralhazard”problemwillcomeintoplay.,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,10,CanPrivateInformationtoAgentBenefitthePrincipal?,0,77,100,0,9,878,10,254,Now,thecontingentsalarycontractwillimprovebyforcingtheAgenttogive(e3=6).,Letusnowlookatthe“privateinformationtoagent”issue!,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,11,CanPrivateInformationtoAgentBenefitthePrincipal?,Thisprivateinformationsystem(onlyobservabletotheagent)generatesthesesignals:,S1,S2,S3,S4,Y1,Y2,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,12,CanPrivateInformationtoAgentBenefitthePrincipal?,Now,thenewprivateinformationmakesiteasyfortheagenttocheat.So,whatshouldtheprincipaldo?,Wouldthenewplanwork?Letuscalculatetheagentsutilityandtheprincipalspayoff.,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,13,0,71.5,100,0,n/a,10,173.5,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,14,Pre-effort“Public”Information?,Thistime,itisdifferentinthattheinformationisavailabletoall,principalandagent.,Thispublicinformationsystem(observabletoall)generatesthesesignals:,S1,S2,S3,S4,Y1,Y2,Isthisinformationusefultotheagent?,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,15,First,theinformationhasnovaluetotheagent.Why?,Thisisbecausetheagent,byobservingY1,cannotguarranteethatthepayoff$25,000willnotoccur.,However,isthiskindofinformationsystemusefultothePrincipal?,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,16,Now,ifY1isobserved,whatwouldtheagentdo?,U(e2)=15,1701/252=98.17U(e3)=15,1701/2*0.5+17,0301/2*0.562=90.89,Thus,thePrincipalinfacttellstheagenttobelazy!,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,17,Then,ifY2isobserved,whatwouldtheagentdo?,U(e2)=15,1701/2*0.5+17,0301/2*0.552=101.88U(e3)=17,0301/2*0.5+21,0741/2*0.562=102.03,Thistime,theagentwillwanttoworkhard.,Onaverage,98.17*0.5+102.03*0.5=100So,thisisacceptabletotheagent.,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,18,ButforthePrincipal,whyshouldhecare?,Notethatthisislargerthan10,254,theoptimalsolutionunderperfectinformation.,Thus,seeminglyuselessinformationcanbeuseful!,Dr.Chak-TongChau,FulbrightGuestLectureMaterials,19,InConclusion,Wecannotguarranteethatpeoplewillalwaysdotheethicallycorrectthings.Therefore,theywillha