In this problem we will ask whether an information cascade can occur if each individual sees only the choice of his immediate neighbor rather than the choices of all those who have chosen previously. Let’s keep the same setup as in the Information Cascades lecture, except that, when individual i chooses, he considers only his own color and the choice of individual i − 1. 1. Briefly explain why the decision problems faced by individuals 1 and 2 are unchanged by this modification to the information network. 2. Individual 3 observes the choices of individual 2, but not the choice of individual 1. What can 3 infer about 2’s color from 2’s choice? 3. Can 3 infer anything about 1’s color from 2’s choice? Explain. 4. What should 3 do if he picks a red ball and he knows that 2 declared Red? What if 3’s picked ball was blue and 2 declared Red? 5. 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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