AI 中文总结
本文针对路径独立选择规则的接受式扩展展开研究，反驳了Chambers和Yenmez2017年的相关定理，构造了特定匹配市场案例，并刻画了允许接受式扩展的选择规则的特征。
AI 中文摘要
若一个选择规则从每个集合X中选出min{q,|X|}个备选方案，则称其为q-接受式规则。我们证明，最大基数至多为q的路径独立规则不一定具有q-接受式路径独立扩展，这反驳了Chambers和Yenmez（2017）的定理4。我们构造了一个单学校匹配市场，其唯一稳定匹配会留下一个席位空缺，而该学校规则的任何路径独立扩展都无法填补这个空缺。每个满足总需求法则的路径独立规则都有这样的扩展。我们通过被拒绝备选方案的单调选择来刻画允许接受式扩展的选择规则。
英文摘要
A choice rule is $q$-acceptant if it chooses $\min\{q,|X|\}$ alternatives from each set $X$. We show that a path-independent rule of maximum cardinality at most $q$ need not have a $q$-acceptant path-independent expansion, refuting Chambers and Yenmez (2017, Theorem 4). We construct a one-school matching market whose unique stable matching leaves a seat vacant that no path-independent expansion of the school's rule fills. Every path-independent rule satisfying the law of aggregate demand has such an expansion. We characterize the choice rules admitting an acceptant expansion by monotone selections of rejected alternatives.
