双边随机匹配市场：延期承兑程序的事前等价性

IF 1.1 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

ACM Transactions on Economics and Computation Pub Date : 2021-10-15 DOI:10.1145/3485010

Simon Mauras

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引用次数: 0

摘要

由N名男性和N名女性组成的群体中的稳定匹配是一个经典的组合问题，自1962年Gale和Shapley的一项开创性工作引入以来，一直是激烈的理论和实证研究的主题。当输入偏好档案由分布生成时，我们研究了两个稳定匹配过程的输出分布：女性提出推迟接受和男性提出推迟接受。我们证明了这两个过程是事前等价的——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，我们推广了（非均匀情况下）一个积分公式，由于Knuth和Pittel，它给出了固定匹配稳定的概率。利用旋转集上的包含-排除原理，我们给出了一个新的公式，该公式给出了固定匹配是女性/男性最优稳定匹配的概率。

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Two-Sided Random Matching Markets: Ex-Ante Equivalence of the Deferred Acceptance Procedures

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 work 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 that gives the probability that a fixed matching is the women/men-optimal stable matching.

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来源期刊

ACM Transactions on Economics and Computation COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-

CiteScore

3.80

自引率

0.00%

发文量

期刊介绍： The ACM Transactions on Economics and Computation welcomes submissions of the highest quality that concern the intersection of computer science and economics. Of interest to the journal is any topic relevant to both economists and computer scientists, including but not limited to the following: Agents in networks Algorithmic game theory Computation of equilibria Computational social choice Cost of strategic behavior and cost of decentralization ("price of anarchy") Design and analysis of electronic markets Economics of computational advertising Electronic commerce Learning in games and markets Mechanism design Paid search auctions Privacy Recommendation / reputation / trust systems Systems resilient against malicious agents.