Dividing Goods or Bads Under Additive Utilities
Dividing Goods or Bads Under Additive Utilities
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在附加效用下划分好坏
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
E. Yanovskaya
中科院分区：
文献类型：
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作者：
Anna Bogomolnaia;H. Moulin;Fedor Sandomirskiy;E. Yanovskaya
当效用是可加的时，我们在之前的论文（Bogomolnaia et al.“Dividing Goods or Bads under Additive Utilities”）中发现了许多相似之处，但也发现了我们在划分（私人）商品或坏品时，熟悉的竞争规则（收入相等）的行为中令人惊讶的差异。在这两种情况下，该规则都会在效率边界上挑选出效用（或非效用）产品的临界点，但如果我们分享商品，则只有一个临界点，而在坏的情况下，可能会有许多个临界点。我们将这种分析扩展到混合项目的公平划分：每个项目可以被一些参与者视为好的，而被其他人视为坏的，具有相应的正或负的边际效用。我们发现，混合物品的划分可以归结为一个全好问题或全坏问题的变体，无论是规范上还是计算上：特别是划分非一次性物品的任务对每个人来说要么是好消息，要么是坏消息。如果至少有一个可行的效用配置文件是积极的，竞争规则挑选唯一的最大值的产品（积极的）效用。如果没有可行的效用剖面是正的，则该规则选择有效边界上的所有非效用乘积的临界点
When utilities are additive, we uncovered in our previous paper (Bogomolnaia et al. "Dividing Goods or Bads under Additive Utilities") many similarities but also surprising differences in the behavior of the familiar Competitive rule (with equal incomes), when we divide (private) goods or bads. The rule picks in both cases the critical points of the product of utilities (or disutilities) on the efficiency frontier, but there is only one such point if we share goods, while there can be exponentially many in the case of bads. We extend this analysis to the fair division of mixed items: each item can be viewed by some participants as a good and by others as a bad, with corresponding positive or negative marginal utilities. We find that the division of mixed items boils down, normatively as well as computationally, to a variant of an all goods problem, or of an all bads problem: in particular the task of dividing the non disposable items must be either good news for everyone, or bad news for everyone. If at least one feasible utility profile is positive, the Competitive rule picks the unique maximum of the product of (positive) utilities. If no feasible utility profile is positive, this rule picks all critical points of the product of disutilities on the efficient frontier