论文标题
双面随机匹配市场：递延接受程序的前ante等效性
Two-Sided Random Matching Markets: Ex-Ante Equivalence of the Deferred Acceptance Procedures
论文作者
论文摘要
自1962年在Gale和Shapley的开创性论文中，自1962年介绍其自1962年介绍以来，在一个由$ n $男性和$ n $女性组成的社区中进行稳定的匹配是一个经典的组合问题。 当从分布中产生输入偏好曲线时，我们研究了两个稳定匹配程序的输出分布：女性偏向于偏向感和男性产生的偏向感。我们表明，这两个过程是同等的：也就是说，在输入分布的某些条件下，它们的输出分布是相同的。 在技术贡献方面，由于Knuth和Pittel，我们将（不均匀的情况）推广（非均匀情况），这给出了固定匹配稳定的概率。我们在旋转集上使用包含 - 排斥原理，给出了一个新的公式，该公式的可能性是固定匹配是女性/男性最佳稳定匹配。我们表明，这两个概率与替换的集成相同。
Stable matching in a community consisting of $N$ men and $N$ women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley. When the input preference profile is generated from a distribution, we study the output distribution of two stable matching procedures: women-proposing-deferred-acceptance and men-proposing-deferred-acceptance. We show that the two procedures are ex-ante equivalent: that is, under certain conditions on the input distribution, their output distributions are identical. In terms of technical contributions, we generalize (to the non-uniform case) an integral formula, due to Knuth and Pittel, which gives the probability that a fixed matching is stable. Using an inclusion-exclusion principle on the set of rotations, we give a new formula which gives the probability that a fixed matching is the women/men-optimal stable matching. We show that those two probabilities are equal with an integration by substitution.
