Cutting a Cake Fairly for Groups Revisited

Erel Segal-Halevi, Warut Suksompong

Research output: Contribution to journalArticlepeer-review


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

All Science Journal Classification (ASJC) codes

  • General Mathematics


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