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How to Cut a Cake Fairly: A Generalization to Groups

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  • Erel Segal-Halevi
  • Warut Suksompong

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.

Suggested Citation

  • Erel Segal-Halevi & Warut Suksompong, 2020. "How to Cut a Cake Fairly: A Generalization to Groups," Papers 2001.03327, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:2001.03327
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    File URL: http://arxiv.org/pdf/2001.03327
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    References listed on IDEAS

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    1. Erel Segal-Halevi & Shmuel Nitzan, 2019. "Fair cake-cutting among families," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 709-740, December.
    2. Azrieli, Yaron & Shmaya, Eran, 2014. "Rental harmony with roommates," Journal of Economic Theory, Elsevier, vol. 153(C), pages 128-137.
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