Cutting a Cake Fairly for Groups Revisited

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-01-13 DOI:10.1080/00029890.2022.2153566

Erel Segal-Halevi, Warut Suksompong

引用次数: 2

Abstract

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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为再次到访的团体公平切蛋糕

蛋糕分割是一个经典的公平分割问题，蛋糕隐喻了一种异构的可分割资源。最近，有研究表明，对于任意数量的玩家对蛋糕有任意偏好，可以将玩家分成任意大小的小组，并将蛋糕分成不同的小组，这样每个小组都能得到一块连续的蛋糕，每个玩家都不会嫉妒。对于两个组，我们描述了可以用有限算法计算这样的分配的组大小，表明了当其中一个组是单例时，任务是可能的。我们还建立了家务分割的一个类似存在性结果，并证明该结果对混合蛋糕不成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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