Envy-Free Cake-Cutting in Two Dimensions

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Presentation transcript:

Envy-Free Cake-Cutting in Two Dimensions EREL SEGAL-HALEVI, AVINATAN HASSIDIM, YONATAN AUMANN erelsgl@cs.biu.ac.il 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 (http://gabrielhemery.com/2010/09/19/birds-eye-view-of-a-growing-woodland/collegefarm_1991), Loiuse K. Oliver (http://sparkyjr.com/17-beautiful-rectangle-birthday-cakes-image-inspirations-3138/beautiful-rectangle-birthday-party-cakes-picture-inspirations/ ) , Derek Jensen (https://commons.wikimedia.org/wiki/File:Warren-indiana-from-above.jpg)