A professor presents a new game to Elsa and her 49 classmates (similar to the situation in Exercise.

A professor presents a new game to Elsa and her 49
classmates (similar to the situation in Exercise S12). As before, each of the
students simultaneously and privately writes down a number between 0 and 100 on
a piece of paper, and the professor computes the mean of these numbers and
calls it X. This time the student who submits the number closest to   wins
$50. Again, if multiple students tie, they split the prize equally.

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(a) Find a symmetric Nash equilibrium to this game. That
is, what number is a best response to everyone else submitting the same number?

(b) Show that choosing the number 5 is a dominated
strategy.

(c) Show that choosing the number 90 is a dominated
strategy.

(d) What are all of the dominated strategies?

(e) Suppose Elsa believes that none of her classmates
will play the dominated strategies found in part

Given these beliefs, what strategies are never a best
response for Elsa?

(f) Which strategies do you think are rationalizable in
this game? Explain your reasoning.

 

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