Question

Q10. In this problem we will explore the power of experts in creating and destroying information cascades. Let's keep the same setup as in lecture and Chapter 16; ordinarily individuals can see the behaviors but not the private signals of all previous individuals. Each individual receives a private signal ("High" or "Low") and must decide whether to Accept or Reject the technology, belief, behavior, practice, etc., in question. To be concrete, let's assume we are talking about a technology-say, a new virtual reality device. Individuals want to Accept Good technology and Reject Bad technology. Good technologies are more likely to generate High private signals; Bad technologies are more likely to generate Low private signals. Finally, suppose we have two types of individuals Ordinary and Expert. Ordinary people have no special knowledge, and so they only get one private signal. Experts have special knowledge relevant to the decision, and so they get two private signals (they always get the same signal-two High or two Low). Assume that everyone knows who is an Expert and who is Ordinary. Everyone also knows that an Expert gets two private signals and an Ordinary person gets only one Imagine that Person 1 is an Expert and Person 2 is Ordinary. Person 1 receives two High signals and Accepts. Person 2 receives a Low signal. What should she do? Explain your answer. (3 points) a. b. Does Person 2's action reveal anything about her private information? Why or why not? (3 points) Now imagine that Person 3,4, 5, etc. arrive and make their decisions. These people are all Ordinary. Explain why an information cascade will occur. (3 points) C. d. Now imagine that after some number of Ordinary people (say 50) another Expert arrives as Person 51. She receives two Low signals. What will she do? Explain your information cascade. (3 points) answer, and the consequences for t he Can an information cascade occur despite multiple Experts acting sequentially? Imagine that Persons 1, 2, and 3 are all Experts. See if you can find a scenario in which an information cascade will nonetheless e. occur and describe it; if such a scenario is impossible, explain why (3 points)

Answer 1

Given :

• Individuals can see the behavior but not the private signals.
• Ordinary people receives one private signal.
• Experts receives two private signals.

Person 1 - Expert

Person 2 - Ordinary

a) Person 1 received two high signals and accepts   

=> Behavior : accept

Person 2 receives low signal and she knows that Person 1 has accepted. Now she has to make a decision based on the signal she received and the behavior of person 1. Since they are different, person 2 will make a decision based on the signal she received. Person 2 will reject.

b) Yes, Person 2 action reveals their private information. Every other person may not be able to see the private information received by others, but they can see others behavior. Person 1 have accepted and person 2 rejected it. The behavior sequence is accept, reject => the behaviors are different, meaning that person 2 took decision based on the information she received => we can conclude that she received low signal.

c) The behavior sequence is accept, reject.

Person 3, 4, 5... arrives (ordinary). Along with private information received, person 3 knows the behavior of person 1 and person 2 => person 3 has three signals (behavior - two; private info - 1).

Person 3 's behavior depends on the majority behavior. Person 1 and person 2 have already made opposite decisions, so person 3 uses her private information to decide. From person 4, everyone can see person 3’s behavior which will also be used for their decisions. (Received information will be used by the ordinary people only when they cant decide anything from previous behaviors otherwise they go for the majority)

d) After 50 ordinary people, 1 expert arrives and receives two low signals. Since experts have special knowledge relevant to the decision, she goes based on the signal received => behavior - reject.

e) Information cascade will not occur as all the experts will decide based on the signal they received. Past behavior will not be taken into account.