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Cutting a Cake Fairly for Groups Revisited

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  • Erel Segal-Halevi
  • Warut Suksompong

Abstract

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.

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  • Erel Segal-Halevi & Warut Suksompong, 2023. "Cutting a Cake Fairly for Groups Revisited," Papers 2301.09061, arXiv.org.
    • Handle: RePEc:arx:papers:2301.09061
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    References listed on IDEAS

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    1. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2017. "Competitive Division of a Mixed Manna," Econometrica, Econometric Society, vol. 85(6), pages 1847-1871, November.
    2. Simmons, Forest W. & Su, Francis Edward, 2003. "Consensus-halving via theorems of Borsuk-Ulam and Tucker," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 15-25, February.
    3. Manurangsi, Pasin & Suksompong, Warut, 2017. "Asymptotic existence of fair divisions for groups," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 100-108.
    4. Suksompong, Warut, 2018. "Approximate maximin shares for groups of agents," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 40-47.
    5. 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.
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