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Lecture

# ECON 221 Fable of the Monks Challenge Problem

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Department
Economics
Course
ECON 221
Professor
Julianna Rogo
Semester
Winter

Description
ECON 221 Game Theory Prof. Juliana Rogo January 15, 2013 Fable of the Monks – Challenge Problem If each monk is supposed to die on the same day they realize they have blue eyes, and they can see each other’s faces but cannot communicate what they see between themselves, then logically, this is what happens: 1. Assume there are only two monks in total and both have the disease. After the announcement is made, will they commit suicide simultaneously? Is yes, in how many days? They will commit suicide simultaneously in 2 days. This is because on the first day, Monk A will see that Monk B has the disease, and assume that Monk B will see that Monk A does not have the disease, and thus Monk B will knowingly commit suicide. But Monk B does not, to Monk A’s surprise commit suicide on the first night. Since Monk B is rational, that can only mean that Monk B thought that Monk A would commit suicide, and thus did not commit suicide himself. For Monk B to think that Monk A would commit suicide reveals to Monk A that he himself must have the disease also. Realizing this, Monk A will commit suicide on the second night. Monk B will go through the same thought process and commit suicide on the second night as well. 2. If there were three monks in total and all of them committed suicide simultaneously? How many monks had the disease and in how many days they committed suicide? All three monks had the disease and they committed suicide in 3 days. This is because Monk C will see Monk A and B and believe that they will commit suicide, once realizing they both have the mark after 2 days. However, to Monk C’s surprise, Monk A and B do not commit suicide in 2 days. That can only mean that they expected Monk C to commit suicide, revealing to C that he has the mark too. Since they all realize they have the disease, all of them will commit suicide on the third night. 3. Suppose you are one of four monks living in the monastery; on the third day after the announcement all the monks (including you) show up for the praying, but the next day only you show up for the praying, how many monks with a mark did you see? Can you say that you are safe from the disease? You saw 3 monks with the mark, and you are safe from the disease. The three monks will have gone through t
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