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,Click to Edit Master Title Style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,Dr.Chak-Tong Chau,Fulbright Guest Lecture Materials,*,Information Systems under Principal-agent Modeling,Dr.Chak-Tong Chau,仇澤棠博士,U.S.Fulbright Professor,中美交流富布萊特教授,What Is Information?,Broadly defined,information,is any device that helps to reduce,uncertainty,.,Alternatively,information should be helpful in:,detecting,the,current,state of the world,or,forecasting,the,future,state of the world,Dr.Chak-Tong Chau,2,Fulbright Guest Lecture Materials,Good Information Should be Useful in:,Improving production decisions telling us to do the right things.,Optimizing the scope for risk sharing so that some people can not make profits by harming other people.,Eliminating“information asymmetry”so that,ex ante,(before-the-act)private information can be known,ex post,(after-the-act).,Dr.Chak-Tong Chau,3,Fulbright Guest Lecture Materials,Time line of a typical agency contract,Contract agreed,Effort selected,Payoff revealed,Pre-contract information,Pre-effort selection information,Post-effort information,Post-payoff information,Timing,Information Availability,To agent only(private),To all parties(public),Pre-contract,Agents proprietary knowledge,Historical information,Post-contract,pre-effort,Information set under decentralization,Post-effort,pre-payoff,Voluntary disclosure relevation principle,Post payoff(,ex post,),Not interesting,Financial reporting,Dr.Chak-Tong Chau,4,Fulbright Guest Lecture Materials,Usefulness of Information,How do we know,a priori,that information is“useful”?,Consider the following payoff structure(known to all):,Effort,S,1,S,2,S,3,S,4,S,5,S,6,Expected Payoff,e,1,=10,2,3,3,4,5,5,3.67,e,2,=5,2,2,3,4,4,5,3.33,Dr.Chak-Tong Chau,5,Fulbright Guest Lecture Materials,Usefulness of Information,Now,we have an information system that will generate these signals:,S,1,S,2,S,3,S,4,S,5,S,6,Y,1,Y,2,Signal:,Y,1,Y,2,S,1,S,2,S,3,S,4,S,5,S,6,e,1,=10,2,3,3,4,5,5,e,2,=5,2,2,3,4,4,5,In a sense,the information system partitions the matrix as follows,Question:Are the signals,Y,1,and Y,2,useful?,Dr.Chak-Tong Chau,6,Fulbright Guest Lecture Materials,Usefulness of Information,Now,we have another information system that will generate these signals:,S,1,S,4,S,5,S,6,Y,1,Y,3,Signal:,Y,1,Y,2,Y,3,S,1,S,2,S,3,S,4,S,5,S,6,e,1,=10,2,3,3,4,5,5,e,2,=5,2,2,3,4,4,5,This new information system partitions the matrix as follows,Question:Are the signals,Y,1,Y,2,and Y,3,useful?,S,2,S,3,Y,2,Dr.Chak-Tong Chau,7,Fulbright Guest Lecture Materials,Can Private Information to Agent Benefit the Principal?,Consider the following payoff structure(known to all):,S,1,S,2,S,3,S,4,Expected Payoff to Principal before Payment to Agent,Prob.,0.25,0.25,0.25,0.25,e,1,=0,0,0,0,0,0,e,2,=5,20,000,20,000,25,000,30,000,23,750,e,2,=6,20,000,30,000,30,000,35,000,28,750,Agents Utility Function:,U=X,-e,2,100,where:X=agents compensationse=the effort level used by the agent,If the Principal can observe effort,how would he pay the agent?,X,-6,2,=100,X,=18,496,Dr.Chak-Tong Chau,8,Fulbright Guest Lecture Materials,Can Private Information to Agent Benefit the Principal?,Now,if the Principal,cannot,observe effort,how would he pay the agent?,How about this compensation contract(a fixed salary of$18,496)to agent?Would this work?,S,1,S,2,S,3,S,4,Expected Utility to A,Expected Payoff to P,Prob.,0.25,0.25,0.25,0.25,e,1,=0,18,496,18,496,18,496,18,496,e,2,=5,18,496,18,496,18,496,18,496,e,3,=6,18,496,18,496,18,496,18,496,136,111,100,-18,496,5,254,10,254,Thus,a fixed salary to someone whom you cannot observe wont work.A“moral hazard”problem will come into play.,Dr.Chak-Tong Chau,9,Fulbright Guest Lecture Materials,Can Private Information to Agent Benefit the Principal?,Now then,what about a,contingent,salary of$18,496 to agent?Would this improve the Principals payoff?,S,1,S,2,S,3,S,4,Expected Utility to A,Expected Payoff to P,Prob.,0.25,0.25,0.25,0.25,e,1,=0,0,0,0,0,e,2,=5,18,496,18,496,0,18,496,e,3,=6,18,496,18,496,18,496,18,496,0,77,100,0,9,878,10,254,Now,the contingent salary contract will improve by forcing the Agent to give(e,3,=6).,Let us now look at the“private information to agent”issue!,Dr.Chak-Tong Chau,10,Fulbright Guest Lecture Materials,CanPrivateInformationtoAgentBenefit thePrincipal?,This,private,informationsystem(onlyobservabletotheagent)generatesthesesignals:,S,1,S,2,S,3,S,4,Y,1,Y,2,Would the,contingent,salary of$18,496 to agent still work?,Signal:,Y,1,Y,2,Expected Utility to Agent with Private info,Expected Payoff to Principal with Private info,S,1,S,2,S,3,S,4,Prob.,0.25,0.25,0.25,0.25,e,1,=0,0,0,0,0,e,2,=5,18,496,18,496,0,18,496,105.5,(,100),7,754,(,10,254,),e,3,=6,18,496,18,496,18,496,18,496,Dr.Chak-Tong Chau,11,Fulbright GuestLectureMaterials,CanPrivateInformationto AgentBenefitthePrincipal?,Now,thenewprivateinformationmakes it easy for the agenttocheat.So,whatshould the principaldo?,Consider this new contingent contract,(corresponding payoffs),:,S,1
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