3. People are trying to decide where to go to dinner and have narrowed their choices to Mama Lucia and Chez Pierre. They do not know which is the better restaurant; with probability 0.5 Mama Lucia is better and with probability 0.5 Chez Pierre is better.

People have read different restaurant reviews. If Mama Lucia is better, then a review will prefer Mama Lucia to Chez Pierre with probability 0.7 and will prefer Chez Pierre to Mama Lucia with probability 0.3. Similarly, if Chez Pierre is better, then a review will prefer Chez Pierre to Mama Lucia with probability 0.7 and will prefer Mama Lucia to Chez Pierre with probability 0.3.

People will make their choices sequentially. Those who have not yet selected a restaurant will see the decisions of those who have already chosen before making their decisions. If someone thinks it is equally likely that Mama Lucia or Chez Pierre is the better choice, she will put a slightly greater weight on the restaurant review she read to break the tie.

a.) Define an information cascade.

b. (15 points) Suppose the first two people choose Mama Lucia. Use Bayes' rule to determine whether or not an information cascade will develop. You will not receive any credit if you do not use Bayes' rule to answer this question.