下降的稳定匹配格：有多少战略代理人需要把悲观到最优？
Descending the Stable Matching Lattice: How many Strategic Agents are required to turn Pessimality to Optimality?
摘要：
稳定匹配集诱导出一个分配格。稳定匹配格的上确界是男孩最优（女孩悲观）稳定匹配，下确界是女孩最优（男孩悲观）稳定匹配。经典的boy建议延迟接受算法返回格的上确界，即boy最优稳定匹配。在本文中，我们研究了最小的一组女孩，称为{ \em最小获胜联盟的女孩}，可以采取战略行动，但独立的，迫使男孩的建议推迟接受算法输出的女孩最佳稳定匹配。我们的特点是最小的获胜联盟在稳定的匹配旋转，并表明其基数可以采取任何值之间的$0$和$\left\lfloor \frac{n}{2}\right\rfloor$，例如与$n$男孩和$n$女孩。我们的主要结果是，对于随机匹配模型，最小获胜联盟的期望基数是$(\frac{1}{2}+o(1))\log{n}$。这解决了Kupfer \cite{Kup18}的一个猜想。
英文摘要：
The set of stable matchings induces a distributive lattice. The supremum of the stable matching lattice is the boy-optimal (girl-pessimal) stable matching and the infimum is the girl-optimal (boy-pessimal) stable matching. The classical boy-proposal deferred-acceptance algorithm returns the supremum of the lattice, that is, the boy-optimal stable matching. In this paper, we study the smallest group of girls, called the {\em minimum winning coalition of girls}, that can act strategically, but independently, to force the boy-proposal deferred-acceptance algorithm to output the girl-optimal stable matching. We characterize the minimum winning coalition in terms of stable matching rotations and show that its cardinality can take on any value between $0$ and $\left\lfloor \frac{n}{2}\right\rfloor$, for instances with $n$ boys and $n$ girls. Our main result is that, for the random matching model, the expected cardinality of the minimum winning coalition is $(\frac{1}{2}+o(1))\log{n}$. This resolves a conjecture of Kupfer \cite{Kup18}.
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。
