Cutting a Cake Fairly for Groups Revisited

Erel Segal-Halevi, Warut Suksompong

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group receives a single contiguous piece and every player is envy-free. For two groups, we characterize the group sizes for which such an assignment can be computed by a finite algorithm, showing that the task is possible exactly when one of the groups is a singleton. We also establish an analogous existence result for chore division, and show that the result does not hold for a mixed cake.

Original languageEnglish
Pages (from-to)203-213
Number of pages11
JournalAmerican Mathematical Monthly
Issue number3
StatePublished - 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 The Author(s). Published with license by Taylor & Francis Group, LLC.


This work was partially supported by the Israel Science Foundation under grant number 712/20, by the Singapore Ministry of Education under grant number MOE-T2EP20221-0001, and by an NUS Start-up Grant. The authors wish to thank the editor and the anonymous reviewers for several constructive comments.

FundersFunder number
National University of Singapore
Ministry of Education - SingaporeMOE-T2EP20221-0001
Israel Science Foundation712/20


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