Envy-Free Cake Divisions Cannot be Found by Finite Protocols

Walter R. Stromquist

92 citations0/0 files storedThe Electronic Journal of Combinatorics

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Game Theory and Voting Systems Game Theory and Applications Optimization and Search Problems

Abstract

We show that no finite protocol (even if unbounded) can guarantee an envy-free division of a cake among three or more players, if each player is to receive a single connected piece.

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References

2000Cake-Cutting Algorithms: Be Fair if You Can.1999Rental Harmony: Sperner's Lemma in Fair Division 1995An Envy-Free Cake Division Protocol 1980How to Cut a Cake Fairly

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2011Optimal Envy-Free Cake Cutting 2009Thou shalt covet thy neighbor's cake 2016A discrete and bounded envy-free cake cutting protocol for four agents

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