当前位置: X-MOL 学术arXiv.cs.GT › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Two New Impossibility Results for the Random Assignment Problem
arXiv - CS - Computer Science and Game Theory Pub Date : 2020-07-14 , DOI: arxiv-2007.07100
Timo Mennle and Sven Seuken

In this note, we prove two new impossibility results for random assignment mechanisms: Bogomolnaia and Moulin (2001) showed that no assignment mechanism can satisfy strategyproofness, ordinal efficiency, and symmetry at the same time, and Mennle and Seuken (2017) gave a decomposition of strategyproofness into the axioms swap monotonicity, upper invariance, and lower invariance. For our first impossibility result, we show that upper invariance, lower invariance, ordinal efficiency, and symmetry are incompatible. This refines the prior impossibility result because it relaxes swap monotonicity. For our second impossibility result, we show that no assignment mechanism satisfies swap monotonicity, lower invariance, ordinal efficiency, anonymity, neutrality, and non-bossiness. By contrasts, the Probabilistic Serial (PS) mechanism that Bogomolnaia and Moulin (2001) introduced, satisfies these axioms when lower invariance is replaced by upper invariance. It follows that there cannot exists a lower invariant counterpart to PS.

中文翻译:

随机分配问题的两个新的不可能结果

在这篇笔记中,我们证明了随机分配机制的两个新的不可能结果: Bogomolnaia 和 Moulin (2001) 表明没有任何分配机制可以同时满足策略证明、序数效率和对称性,而 Mennle 和 Seuken (2017) 给出了分解将策略证明转换为公理交换单调性、上不变性和下不变性。对于我们的第一个不可能结果,我们表明上不变性、下不变性、序数效率和对称性是不相容的。这改进了先前的不可能结果,因为它放宽了交换单调性。对于我们的第二个不可能结果,我们表明没有任何分配机制满足交换单调性、较低的不变性、有序效率、匿名性、中立性和非老板性。相比之下,Bogomolnaia 和 Moulin (2001) 引入的概率序列 (PS) 机制在下不变性被上不变性取代时满足这些公理。因此,不存在 PS 的较低不变性对应物。
更新日期:2020-07-15
down
wechat
bug