论文标题
与有限能力的稳定匹配的连续模型
A Continuum Model of Stable Matching With Finite Capacities
论文作者
论文摘要
本文介绍了稳定匹配的统一框架，该框架嵌套了有限市场中稳定匹配的传统定义，以及Azevedo和Leshno（2016）的稳定匹配的连续定义作为特殊情况。在此框架内，我确定了一种新型的连续模型，该模型做出了个人级别的概率预测。 这个新模型始终具有独特的稳定结果，可以使用递延接受算法的类似物找到。该模型与Azevedo和Leshno（2016）的模型之间的关键差异是，他们认为每所学校的学生权益数量都是确定性的，而我的建议替代方案假设它遵循泊松分布。结果，这个新模型可以准确地预测截止的模拟分布，即使对于只有十所学校和二十名学生的市场也是如此。 该模型生成了有关比赛的数量和质量的新见解。当学校均匀时，它为学生的平均水平提供了上限和下限，这与Ashlagi，Kanoria和Leshno（2017）相匹配，但适用于更一般的环境。该模型还为Marx和Schummer（2021）考虑的平台定价设置中的匹配次数提供了干净的分析表达式。
This paper introduces a unified framework for stable matching, which nests the traditional definition of stable matching in finite markets and the continuum definition of stable matching from Azevedo and Leshno (2016) as special cases. Within this framework, I identify a novel continuum model, which makes individual-level probabilistic predictions. This new model always has a unique stable outcome, which can be found using an analog of the Deferred Acceptance algorithm. The crucial difference between this model and that of Azevedo and Leshno (2016) is that they assume that the amount of student interest at each school is deterministic, whereas my proposed alternative assumes that it follows a Poisson distribution. As a result, this new model accurately predicts the simulated distribution of cutoffs, even for markets with only ten schools and twenty students. This model generates new insights about the number and quality of matches. When schools are homogeneous, it provides upper and lower bounds on students' average rank, which match results from Ashlagi, Kanoria and Leshno (2017) but apply to more general settings. This model also provides clean analytical expressions for the number of matches in a platform pricing setting considered by Marx and Schummer (2021).
