information systems and principal agent models

1、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,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,2,What Is Information?,Broadly defined, information is

2、 any device that helps to reduce uncertainty.Alternatively, information should be helpful in:detecting the current state of the world, orforecasting the future state of the world,Dr. Chak-Tong Chau,Fulbright Guest L

3、ecture Materials,3,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 oth

4、er 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,Fulbright Guest Lecture Materials,4,,,,,Time line of a typica

5、l agency contract,Contract agreed,Effort selected,Payoff revealed,Pre-contract information,Pre-effort selection information,Post-effort information,Post-payoff information,Dr. Chak-Tong Chau,Fulbright Guest Lecture Mater

6、ials,5,Usefulness of Information,How do we know, a priori, that information is “useful”?,Consider the following payoff structure (known to all):,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,6,Usefulness of Inform

7、ation,Now, we have an information system that will generate these signals:,{S1, S2, S3},{S4, S5, S6},Y1,Y2,,,In a sense, the information system partitions the matrix as follows,Question: Are the signals, Y1 and Y2, usefu

8、l?,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,7,Usefulness of Information,Now, we have another information system that will generate these signals:,{S1},{S4, S5, S6},Y1,Y3,,,This new information system partitio

9、ns the matrix as follows,Question: Are the signals, Y1,,Y2 and Y3 useful?,{S2, S3},Y2,,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,8,Can Private Information to Agent Benefit the Principal?,Consider the following

10、 payoff structure (known to all):,Agent’s Utility Function: U = X½ - e2 ? 100 where: X = agent’s compensationse = the effort level used by the agent,If the Principal can observe effort, how would he pay the agen

11、t?,X ½ - 62 = 100,,X = 18,496,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,9,Can Private Information to Agent Benefit the Principal?,Now, if the Principal cannot observe effort, how would he pay the agent?,1

12、36,111,100,-18,496,5,254,10,254,Thus, a fixed salary to someone whom you cannot observe won’t work. A “moral hazard” problem will come into play.,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,10,Can Private Inform

13、ation to Agent Benefit the Principal?,0,77,100,0,9,878,10,254,Now, the contingent salary contract will improve by forcing the Agent to give (e3 = 6).,Let us now look at the “private information to agent” issue!,,Dr. Chak

14、-Tong Chau,Fulbright Guest Lecture Materials,11,Can Private Information to Agent Benefit the Principal?,This private information system (only observable to the agent) generates these signals:,{S1, S2},{S3 ,S4},Y1,Y2,,,Dr

15、. Chak-Tong Chau,Fulbright Guest Lecture Materials,12,Can Private Information to Agent Benefit the Principal?,Now, the new private information makes it easy for the agent to cheat. So, what should the principal do?,,Woul

16、d the new plan work? Let us calculate the agent’s utility and the principal’s payoff.,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,13,0,71.5,100,0,n/a,10,173.5,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials

17、,14,Pre-effort “Public” Information?,This time, it is different in that the information is available to all, principal and agent.,This public information system (observable to all) generates these signals:,{S1, S2},{S3 ,

18、S4},Y1,Y2,,,Is this information useful to the agent?,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,15,First, the information has no value to the agent. Why?,This is because the agent, by observing Y1, cannot guarr

19、antee that the payoff $25,000 will not occur.,However, is this kind of information system useful to the Principal?,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,16,Now, if Y1 is observed, what would the agent do?,

20、U(e2) = 15,1701/2 – 52 = 98.17U(e3) = 15,1701/2*0.5 +17,0301/2*0.5 – 62 = 90.89,Thus, the Principal in fact tells the agent to be lazy!,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,17,Then, if Y2 is observed, wh

21、at would the agent do?,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 = 102.03,This time, the agent will want to work hard.,On average, 98.17*0.5 + 102.03*0.5 = 100So, th

22、is is acceptable to the agent.,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,18,But for the Principal, why should he care?,Note that this is larger than 10,254, the optimal solution under perfect information.,Thus

23、, seemingly useless information can be useful!,Dr. Chak-Tong Chau,Fulbright Guest Lecture Materials,19,In Conclusion,,We cannot guarrantee that people will always do the ethically correct things.Therefore, they will hav

24、e to be monitored and controlled.Information systems provide us with the means to:inform us what has happened, andmotivate people to do the ethically correct things.It is therefore important to consider these points