1. Envy-Free Cake-Cutting in Two Dimensions
EREL SEGAL-HALEVI, AVINATAN HASSIDIM, YONATAN AUMANN
1. “Divide the land equally” (Ez. 47:14)
n people with different tastes
Land is heterogeneous
How to divide the land fairly?
2. Cake Cutting
Standard model of fair division:
“W.l.o.g, the cake is the interval [0,1]”.
1-dimensional model.
Classic protocols.
3. From 1-D to 2-D
Each agent gets a useless thin sliver!
4. Usable plots
How to divide the land fairly into plots with usable 2-D shape?
5. This paper
All plots have usable shapes (squares)
The cake is two-dimensional
Envy-free
Utility per agent above given threshold
6. Results
* Last two lines do not appear in the proceedings version
Entire land
Plots
Agents
Utility
Upper bound
Square
squares 2
1/4
Plane
¼-plane
1/2 3
1/10
1/6
1/3 n
1/O(n2)
1/(2n) 4
7. New geometric techniques - two dimensional knives
Photo credits: Gabriel Hemery ( Loiuse K. Oliver ( ) , Derek Jensen (