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稳定匹配的注意力成本

The Attention Cost of Stable Matching

Victor H. Aguiar, Dian Hong

arXiv 2609.09693首次发表:更新:

发表机构

Simon Fraser University(西蒙菲莎大学)

机构由 AI 辅助整理,请以论文原文为准。

AI 中文总结

本文研究大市场中注意力稀缺对稳定匹配的影响,提出有限注意力延迟接受算法,并通过速配和智利学校选择数据验证了其减少分配损失、保留有效授权的效果。

AI 中文摘要

在大市场中,稀缺的注意力限制了伴侣评估并造成分配损失,而稳定性会放大这种损失。在一个平均可执行度为 $d$ 的独立随机市场中,在稳定匹配下未匹配份额以 $e^{-\sqrt d}$ 的速率下降,而在同一图上的最大匹配下则以 $e^{-d}$ 的速率下降。改变考虑集可以使在临时活跃屏幕计算中被拒绝的申请重新变得相关。精确的查询中立实现必须保留与分配相关的屏幕外授权;否则,缺失的授权必须重新获取。有限注意力延迟接受(LA-DA)保留有效授权并重新激活符合条件的配对。在精确的次优信息和持久执行权条件下,自适应发现相对于独立暴露在达到的提案数量上节省了一个对数因子。在速配的应用中,双边报告使我们能够在受限图上比较稳定匹配和最大匹配,从而将错失的机会与同图稳定性损失区分开来。在智利的学校选择中,我们记录了9,502名申请人通过保留排名接受了排名更高或新的安置。

英文摘要

In large markets, scarce attention limits partner evaluation and creates allocation loss, which stability magnifies. In an independent random market with average executable degree $d$, unmatched shares fall at rates $e^{-\sqrt d}$ under stability and $e^{-d}$ under maximum matching on the same graph. Changing consideration can make applications rejected in a provisional active-screen computation relevant again. Exact query-neutral implementation must retain allocation-relevant off-screen authorizations; otherwise, missing authorization must be reacquired. Limited-attention deferred acceptance (LA-DA) preserves valid authorizations and reengages eligible pairs. Conditional on exact next-best information and persistent execution rights, adaptive discovery saves a logarithmic factor in reached proposals relative to independent exposure. In an application to speed dating, bilateral reports let us compare stable and maximum matching on restricted graphs, separating missed opportunities from same-graph stability loss. In Chilean school choice, we document 9,502 applicants accepting higher-ranked or new placements through retained rankings.

Comments21 pages of main text; 48 pages including appendices and references

论文原文

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