Warm Up – 2/24 - Monday Five players are dividing a cake using the lone- Divider Method. 𝑃 5 divides the cake. The bid sets are as follows. 𝑃 1 − 𝑠 2 , 𝑠 4 𝑃 2 − 𝑠 2 , 𝑠 4 𝑃 3 − 𝑠 2 , 𝑠 3 , 𝑠 5 𝑃 4 −{ 𝑠 2 , 𝑠 3 , 𝑠 4 } What is 𝑃 5 ’s bidset? Which slice does 𝑃 3 have to take? Why? How many fair divisions can be made? Why no more?

Chapter So-Far Fair Division Divider-Chooser (2 players) Fair means everyone gets what a fair share based on their own value system Divider-Chooser (2 players) Lone Divider (More than 2 players) One person divides, the other players bid Ties are settled by Divider-Chooser Lone Chooser (More than 2 players) One person chooses at the end Other Players ensure they get at least a fair share

Lone-Chooser Example Angela, Boris, and Carlos will split a strawberry-vanilla cake using Lone-Chooser. Above is how they value the cake. Label each side of the cake in terms of how much the person likes that side.

Angela cuts the cake… Into two shares, 𝑠 1 120° 𝑜𝑓 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑦 and 𝑠 2 (60° 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑦, 180° 𝑣𝑎𝑛𝑖𝑙𝑙𝑎). 1. Which share will Boris pick? 2. How will Boris subdivide his share? 3. How will Angela subdivide her share? 4. Which pieces will Carlos select?

Lone-Chooser Classwork