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Maximin Envy-Free Division of Indivisible Items

机译:Maximin羡慕的不可分割项目

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摘要

Assume that two players have strict rankings over an even number of indivisible items. We propose two algorithms to find balanced allocations of these items that are maximin-maximize the minimum rank of the items that the players receive-and are envy-free and Pareto-optimal, if such allocations exist. To determine whether an envy-free allocation exists, we introduce a simple condition on preference profiles; in fact, our condition guarantees the existence of a maximin, envy-free, and Pareto-optimal allocation. Although not strategy-proof, our algorithms would be difficult to manipulate unless a player has complete information about its opponent's ranking. We assess the applicability of the algorithms to real-world problems, such as allocating marital property in a divorce or assigning people to committees or projects.
机译:假设两个玩家在偶数个不可分项目上都有严格的排名。我们提出了两种算法来找到这些项目的平衡分配,这些算法最大程度地最大化了玩家收到的项目的最小等级,并且如果存在这样的分配,那么它们是无羡慕的且帕累托最优的。为了确定是否存在羡慕的分配,我们在偏好配置文件中引入了一个简单条件;实际上,我们的条件保证了极大值,无羡慕和帕累托最优分配的存在。尽管不是策略性的,但除非玩家掌握有关其对手排名的完整信息,否则我们的算法将难以操作。我们评估算法在现实世界中问题的适用性,例如在离婚中分配婚姻财产或将人分配到委员会或项目。

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