mgf1107lecture6 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 6 Chapter 3 – The Mathematics of Sharing If 20 pieces of Halloween candy are to be split between four children, then it seems obvious to award five pieces to each child. However if the candies are all different, and some are clearly more desirable than others, then the method of apportioning the candy becomes less obvious. Similarly, if 10 players are to be split between two soccer teams, then some consideration has to be given to the ability of each player in order for the division to be fair. This chapter turns the process of sharing into a mathematical problem, and we will discuss several proposed methods. Definitions i) The item or items being divided are called the goods , and are collected denoted by S. ii) The people dividing the goods are called the players . Assumptions i) We assume that each player places an intrinsic value on each good, either absolutely (“this good, to me, is worth $100”) or relatively (“this good, to me, is worth 30% of S”). ii) We assume that players act rationally
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This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.

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mgf1107lecture6 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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