arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.00600cs.GT
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激励相容的森林选择机制

Incentive-Compatible Selection Mechanisms for Forests

Yakov Babichenko, Oren Dean, Moshe Tennenholtz

摘要:

给定有向森林图,概率\emph{selection mechanism}是顶点集上的概率分布。选择机制是\emph{incentive-compatible}(IC),如果分配给顶点的概率在我们改变它的输出边(甚至删除它)时不改变。选择机制的质量是在该机制分布下的期望子代与森林中的最大子代之间的最坏情况比率。在本文中,我们证明了一个上界的4/5和$ 1/\ln16\approx0.36 $的任何IC选择机制的质量的下限。通过两种新的机制实现了下限,并且是对Babichenko等人(WWW '18)的结果的显著改进。第一种机制更简单,具有生成公平分布的良好特性(即,单调和比例)。这种机制的缺点是它不精确(即,概率可能加起来小于1)。我们的第二个机制,更复杂,是准确的,但不公平。我们还证明了一个IC机制,是准确和公平的,并具有积极的品质是不可能的。

英文摘要:

Given a directed forest-graph, a probabilistic \emph{selection mechanism} is a probability distribution over the vertex set. A selection mechanism is \emph{incentive-compatible} (IC), if the probability assigned to a vertex does not change when we alter its outgoing edge (or even remove it). The quality of a selection mechanism is the worst-case ratio between the expected progeny under the mechanism's distribution and the maximal progeny in the forest. In this paper we prove an upper bound of 4/5 and a lower bound of $ 1/\ln16\approx0.36 $ for the quality of any IC selection mechanism. The lower bound is achieved by two novel mechanisms and is a significant improvement to the results of Babichenko et al. (WWW '18). The first, simpler mechanism, has the nice feature of generating distributions which are fair (i.e., monotone and proportional). The downside of this mechanism is that it is not exact (i.e., the probabilities might sum-up to less than 1). Our second, more involved mechanism, is exact but not fair. We also prove an impossibility for an IC mechanism that is both exact and fair and has a positive quality.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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