← 研踪 PaperTrailarXiv:2611.06175 · v1
One Strategic Woman: Sharp Ranks and a Persistent Core
首次提交 2026-11-04 16:55
版本更新 2026-11-04 16:55
雷达观测 2026-11-05 11:10
摘要
In a balanced random stable-marriage market, one fixed woman manipulates men-proposing deferred acceptance to obtain her best attainable partner. We prove that the women's expected average true partner rank is asymptotic to $(\ln n)^2$, improving the previous $O((\ln n)^4)$ bound, while the men's is asymptotic to $n/(2\ln n)$. The men's and women's average ranks, normalized by $n/\ln n$ and $\ln n$, converge jointly in distribution to $(U,U^{-1})$, where $U$ is uniform on $(0,1)$. Under optimal truthful truncation, the span of women's average ranks within the reported stable core, divided by $\ln n$, converges in distribution to $U^{-1}-1$.
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v1 · 2026-11-04 16:55 · 最新观测版本
One Strategic Woman: Sharp Ranks and a Persistent Core
In a balanced random stable-marriage market, one fixed woman manipulates men-proposing deferred acceptance to obtain her best attainable partner. We prove that the women's expected average true partner rank is asymptotic to $(\ln n)^2$, improving the previous $O((\ln n)^4)$ bound, while the men's is asymptotic to $n/(2\ln n)$. The men's and women's average ranks, normalized by $n/\ln n$ and $\ln n$, converge jointly in distribution to $(U,U^{-1})$, where $U$ is uniform on $(0,1)$. Under optimal truthful truncation, the span of women's average ranks within the reported stable core, divided by $\ln n$, converges in distribution to $U^{-1}-1$.
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