Optimal Fair Division for Measures with Piecewise Linear Density Functions

Jerzy Legut

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Optimal Fair Division for Measures with Piecewise Linear Density Functions

机译：具有分段线性密度函数的度量的最优公平划分

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摘要

A nonlinear programming method is used for finding an optimal fair division of the unit interval [0,1) among n players. Preferences of players are described by nonatomic probability measures with piecewise linear (PWL) density functions. The presented algorithm can be applied for obtaining "almost" optimal fair divisions for measures with arbitrary density functions approximable by PWL functions. The number of cuts needed for obtaining such divisions is given.

机译：非线性编程方法用于找到n个玩家之间的单位间隔[0,1）的最佳公平分配。玩家的偏好通过具有分段线性（PWL）密度函数的非原子概率度量来描述。所提出的算法可以用于获得“几乎”最优公平划分，用于具有可通过PWL函数近似的任意密度函数的度量。给出了获得这种划分所需的削减数量。

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来源
《International game theory review》 |2017年第2期|1750009.1-1750009.12|共12页
作者
Jerzy Legut;
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作者单位

Department of Mathematics Wroclaw University of Technology Wroclaw, Poland;

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原文格式 PDF
正文语种 eng
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关键词
Fair division; cake cutting; optimal partitioning of a measurable space;

机译：公平划分;切蛋糕;可测量空间的最佳划分;

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Optimal Fair Division for Measures with Piecewise Linear Density Functions

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