How to Cut a Cake Fairly: A Generalization to Groups

Erel Segal-Halevi, Warut Suksompong

Research output: Contribution to journalComment/debate

7 Scopus citations

Abstract

A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious. We generalize this result by showing that it is possible to partition the players into groups of any desired sizes and divide the cake among the groups so that each group receives a single contiguous piece, and no player finds the piece of another group better than that of the player’s own group.

Original languageEnglish
Pages (from-to)79-83
Number of pages5
JournalAmerican Mathematical Monthly
Volume128
Issue number1
DOIs
StatePublished - 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021, THE MATHEMATICAL ASSOCIATION OF AMERICA.

Funding

This work was partially supported by the Israel Science Foundation (grant no. 712/20), by the European Research Council (ERC) under grant number 639945 (ACCORD), and by an NUS Start-up Grant. We would like to thank Steven Brams, Walter Stromquist, Rodrigo Velez, as well as the editor and anonymous reviewers for helpful feedback. 1

FundersFunder number
European Research Council639945
National University of Singapore
Israel Science Foundation712/20

    Keywords

    • MSC: Primary 91B10
    • Secondary 91B14

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