Week2ProblemAndres

# Week2ProblemAndres - 1 Eating Pizza There are three...

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1. Eating Pizza: There are three roommates, Alex, Ben and Chris (denote them by A,B,C), in a college dorm. One evening, they are arguing how to divide a pizza that was just delivered. Suppose that the pizza has size 1 . They divide the pizza according to the following protocol: Period 1: (i) Alex cuts the pizza into two pieces (ii) Ben chooses one out of the two pieces. Alex eats the piece of pizza that Ben did NOT choose. Period 2: (iii) Ben cuts the remaining pizza into two pieces (iv) Chris chooses one out of the two pieces. Ben eats the piece of pizza that Chris did NOT choose. Period 3: (v) Chris eats the remaining pizza Let W; X; Y be the size of the pizza for Alex, Ben, Chris respectively. No pizza is left over, so we have W + X + Y = 1 . Their payo/s are simply the amount of pizza they eat. Answer the following questions: (a) Suppose that 4 5 of the pizza is left at the beginning of period 2 . What is the optimal way to cut the remaining pizza for Ben? Suppose Ben cut the

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Week2ProblemAndres - 1 Eating Pizza There are three...

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