In this problem we ask whether an information cascade can occur if each individual sees only the action of his immediate neighbor rather than the actions of all those who have chosen previously. Let’s keep the same setup as in Chapter 16, except than when individual i chooses he observes only his own signal and the action of individual i − 1.
(a) Briefly explain why the decision problems faced by individuals 1 and 2 are unchanged by this modification to the information network.
(b) Individual 3 observes the action of individual 2, but not the action of individual 1. What can 3 infer about 2’s signal from 2’s action?
(c) Can 3 infer anything about 1’s signal from 2’s action? Explain.
(d) What should 3 do if he observes a high signal and he knows that 2 accepted? What if 3’s signal was low and 2 accepted?
(e) Do you think that a cascade can form in this world? Explain why or why not. A formal proof is not necessary; a brief argument is sufficient.
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