论文标题
如何公平切割离散的蛋糕
How to cut a discrete cake fairly
论文作者
论文摘要
蛋糕切割是划分异质资源的基本模型，例如土地，广播时间和广告空间。在这项研究中，我们考虑了将离散蛋糕分开的问题，在该问题中，不可分割的商品在路径上保持一致，并且代理有兴趣接收连接的物品子集。我们证明，不可分割的不可分割的项目满足了嫉妒柔性的离散物，称为嫉妒柔性，最高为一种善良（EF1），对于任何具有单调估值的代理商n始终存在。我们的结果解决了Bilò等人提出的一个公开问题。 （2019年），他证明了代理数量最多总是存在EF1连接的划分。此外，可以扩展证明以显示以下（1）秘密和（2）额外的版本：（1）n个具有单调估值的n个代理商，可以将路径划分为n可以通过n互联的构造，以使其他ef fors for for not for note for noters fors for node node node nobers forshode septions bude node sodement fore the Reples buds buds buds bude bude bude nections bunded bunde nections bunded bunds bude nections。 （2）对于具有单调估值的N+1个代理，可以将路径分为N连接的捆绑包，以便在任何额外的代理离开时，可以将束的EF1分配给其余代理。
Cake-cutting is a fundamental model of dividing a heterogeneous resource, such as land, broadcast time, and advertisement space. In this study, we consider the problem of dividing a discrete cake fairly in which the indivisible goods are aligned on a path and agents are interested in receiving a connected subset of items. We prove that a connected division of indivisible items satisfying a discrete counterpart of envy-freeness, called envy-freeness up to one good (EF1), always exists for any number of agents n with monotone valuations. Our result settles an open question raised by Bilò et al. (2019), who proved that an EF1 connected division always exists for the number of agents at most 4. Moreover, the proof can be extended to show the following (1) secretive and (2) extra versions: (1) for n agents with monotone valuations, the path can be divided into n connected bundles such that an EF1 assignment of the remaining bundles can be made to the other agents for any selection made by the secretive agent; (2) for n+1 agents with monotone valuations, the path can be divided into n connected bundles such that when any extra agent leaves, an EF1 assignment of the bundles can be made to the remaining agents.
