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arXiv · 2301.09061

Cutting a Cake Fairly for Groups Revisited

Erel Segal-Halevi·Warut Suksompong
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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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BibTeXRIS

Erel Segal-Halevi, Warut Suksompong. 2023-01-22. Cutting a Cake Fairly for Groups Revisited. https://doi.org/10.1080/00029890.2022.2153566

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