Question: Suppose you and your friend Amy work together to develop a unique magic trick that either of you could perform alone. It turns out to

Suppose you and your friend Amy work together to develop a unique magic trick that either of you could perform alone. It turns out to be a tremendously popular trick and both of you make it big as professional magicians. Suppose you decide to conspire together and limit the number of performances featuring the trick. If both of you do only one show a week, each of you earns a profit of $10,000 for that show. If both of you do five shows a week, each of you earns a total profit of $6,000. If one does a single show while the other does five shows, the former gets a profit of $1,000 and the latter gets a profit of $15,000.
a. Use this information to complete the table.

b. Suppose Amy does one show. What is your preferred strategy?
c. Suppose Amy does five shows. What is your preferred strategy?
d. What is your dominant strategy?
e. Suppose you do one show. What is Amy's preferred strategy?
f. Suppose you do five shows. What is Amy's preferred strategy?
g. What is Amy's dominant strategy?
h. What is the Nash equilibrium?
i. Magicians are famously hesitant to reveal the secrets behind their magic, even to other magicians. Based on what you've learned in this question, why do they act like this? Is letting other magicians in on your secrets an optimal strategy?

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