FAIR division (Txt: 3.1 & SOL: DM.7) Classwork: Read p. 76-77 p. 103 (1, 5, 7, 9, 11) Homework (day 21): p. 103 (2, 6, 8, 10, 12) or www.mathxlforschools

Fair Division Project- Due Day 27

Introduction to Fair Divison http://media.pearsoncmg.com/cmg/pmmg_mml_shared/flash_vi deo_player/player.html?ph/esm/esm_tannenbaum_excursions_7/ video/tem07_03_intro

Basic Assumption Rational- each player is a thinking, rational entity seeking to maximize their share of the booty. Cooperation- players are willing participants an accept the rules of the game as binding. Privacy- players do not have any useful information on the players value system and/or any kinds of moves others are going to make. Symmetry- players have equal right in sharing.

Basic Elements of Fair Division The goods “booty”- the item(s) being divided. Denoted “s” in the book The players- a set of parties with the right to share the booty The value system- the fundamental assumption that each player has an internalized value system that gives the player the ability to quantify the value of the booty or any of its parts. (i.e. The player assigns the booty a value: Absolute terms- to me it is worth $50 Relative terms- to me it is worth 30% of the total value of the booty https://www.youtube.com/watch?v=e7WO1lwW36s https://www.youtube.com/watch?v=3avEE3TXCBE&list =PLEA12CF1D59C128E6

Cake Division Scheme For 𝑛 players, it will e proportional if each player’s strategy guarantees him a piece of a given size or value that I sat least 1 𝑛 of the whole in his own estimation. This will be what is considered ENVY- FREE https://www.youtube.com/watch?v=3avEE3TXCBE &list=PLEA12CF1D59C128E6

Cake Division Everyone will survey the cake. This is a procedure that the players can use to allocate a cake among themselves so that each player has a strategy that will guarantee him/her a piece of collision by the others. Everyone will survey the cake. Everyone will come up with their own way to fairly divide the cake. Dividing (dividor)- person cutting (What he/she thinks is fair) Each person will present their Idea of what is the fair way to divide the cake. What is fair? Everyone has their perspective & what you have to consider everyone’s perspective. Choosing- what the other person would choose.

Ex: You value chocolate five times as much as vanilla Ex: You value chocolate five times as much as vanilla. The cake is worth $24. A) How much is the chocolate half worth? How much is the vanilla half worth? $12 and $12 B) How much is a slice formed by 30 𝑜 vanilla and 70 𝑜 chocolate? C) If the cake is cut into six slices each forming a 60 𝑜 , how much is each slice worth? D) If the cake is cut into eight slices (four of each flavor), how much are two slices of chocolate worth?

Answers HW p. 103 (2, 6, 8, 10, 12)