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Problem dealing with cutting a cake and personal choices
There is a cake that is half lemon and half coffee. Steve values a whole
lemon cake at $6, and a whole coffee cake at $10. Kevin values a
whole lemon cake at $6 and a whole coffee cake at $4. Professor
Raiffa suggests that they should divide the cake by selecting one
person to cut the cake any way they like and the other person to choose
whatever piece he prefers.
a. If Steve is selected to cut the cake, and he does not know Kevin's
preferences, how should he cut the cake (assuming he is rationally
trying to maximize his expected value)? What will the outcome be
for both players? Suggestion: draw the cake and show the cut line.
Why did Steve make that cut? What was he thinking?
b. If Steve knows Kevin's preferences, then how will Steve cut the
cake? Explain the difference between the strategy and outcomes
for this situation as opposed to the one in part a. (Hint: your cut
does not necessarily have to be either a straight line across the cake
or a cut through the center).
c. In a situation where the players don't know each others'
preferences, is it better to be the cutter or the chooser? Why?
d. In a situation where the players do know each others preferences,
is it better to be the cutter or the chooser? Why?
This is a game theory problem regarding cake cutting.