捐赠物品消除嫉妒的多变量模型
Multivariate Algorithmics for Eliminating Envy by Donating Goods
摘要：
在某些应用中，将一组不可分割的资源公平地分配给一组代理是至关重要的。然而，在分配实施后，代理人的偏好可能会改变，嫉妒可能会出现。我们研究以下问题来应对此类情况：给定将不可分割的资源分配给具有基于附加效用的偏好的代理，是否有可能在社会上捐赠一些资源（这意味着从分配实例中删除这些资源），以便得到修改后的分配是无羡慕的（最多一件商品）。我们要求被删除的资源的数量和/或所造成的功利福利损失的分配是有界的。我们对这个问题的（参数化的）计算复杂性进行了彻底的研究，考虑了各种自然和问题特定的参数（例如，代理数量、删除的资源数量或初始分配中分配给代理的最大资源数量）和不同的偏好模型，包括一元和0/1估值。在我们的研究中，我们获得了一组丰富的（参数化）易处理性和棘手性的结果，并发现了几个令人惊讶的对比，例如，两个密切相关的公平性概念之间的嫉妒-免费和嫉妒-免费高达一个好的和之间的影响的参数最大数量和福利的删除资源。
英文摘要：
Fairly dividing a set of indivisible resources to a set of agents is of utmost importance in some applications. However, after an allocation has been implemented the preferences of agents might change and envy might arise. We study the following problem to cope with such situations: Given an allocation of indivisible resources to agents with additive utility-based preferences, is it possible to socially donate some of the resources (which means removing these resources from the allocation instance) such that the resulting modified allocation is envy-free (up to one good). We require that the number of deleted resources and/or the caused utilitarian welfare loss of the allocation are bounded. We conduct a thorough study of the (parameterized) computational complexity of this problem considering various natural and problem-specific parameters (e.g., the number of agents, the number of deleted resources, or the maximum number of resources assigned to an agent in the initial allocation) and different preference models, including unary and 0/1-valuations. In our studies, we obtain a rich set of (parameterized) tractability and intractability results and discover several surprising contrasts, for instance, between the two closely related fairness concepts envy-freeness and envy-freeness up to one good and between the influence of the parameters maximum number and welfare of the deleted resources.
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