School Choice with Control and Bayesian School Choice

该奖项资助了匹配机制的经济学理论研究。其目标是开发可用于解决现有问题的新方法。最近，许多经济理论家解决了所谓的“择校问题”。这个问题的起因是美国一些公立学区决定采用新的学生分配制度。传统上，“边界系统”设定了地理边界，边界内的所有学生都在同一所学校就读。在选择系统中，家庭有机会向中央信息交换中心提交一份首选学校作业清单。然后，该交换所将学生与学校进行匹配；该交换所用来从偏好列表到作业的一套规则被称为匹配机制。PI正在开发新的机制，可以在两种不同的现实世界中使用。首先，他们开发了一种机制，当作业不仅必须考虑家庭偏好，而且必须考虑地区范围的多样性目标时，可以使用这种机制。其次，他们开发了一种机制，在这种情况下，家庭不仅可以从最喜欢的学校到最不喜欢的学校列出他们喜欢的学校，还可以说出他们有多想要他们最喜欢的学校。这项研究有两个技术部分。私人投资倡议提出了一种解决多样性问题的一般方法，将一些具体政策作为特例予以承认。PI构造的选择规则考虑了多样性目标，并在这些选择规则满足替代项、被拒绝学生的无关性和总需求定律时进行学习；所有这些都是延迟接受算法产生稳定匹配的关键，具有理想的性质。第二部分通过考虑对学校有私人评价的学生，在择校问题中纳入了不完全的基本信息。学生可以有不同的学校排名，而一些学校可能比其他学校更受欢迎。在这种情况下，研究表明，波士顿机制并不总是比延期接受算法产生更高的社会福利。该项目还包括揭示这些机制的一般结构和分析贝叶斯分配博弈的研究，贝叶斯分配博弈是另一类择校问题。

This award funds research in the economic theory of matching mechanisms. The goal is to develop new methods that can be employed to solve existing problems.The so called "school choice problem" has recently been tackled by a number of economic theorists. The problem is motivated by decisions made by a number of public school districts in the US to adopt new systems for assigning students to schools. Traditionally, a 'boundary system' sets geographic boundaries and all students inside the boundary attend the same school. In a choice system, families have the opportunity to submit a list of preferred school assignments to a central clearinghouse. That clearinghouse then matches students to schools; the set of rules that the clearinghouse uses to go from preference lists to assignments is called a matching mechanism. The PIs are developing new mechanisms that can be used in two different real world situations. First, they develop a mechanism that can be used when assignments must take into account not just family preferences but also district-wide diversity goals. Second, they develop a mechanism for cases where families do not just list their preferred schools from most preferred to least preferred, but are also able to state just how much they want their most preferred school.There are two technical components to the research. The PIs propose a general approach to diversity concerns that admits a number of specific policies as special cases. The PIs construct choice rules that take the diversity objectives into account and study when these choice rules satisfy substitutes, irrelevance of rejected students and the law of aggregate demand; all of which are crucial for the deferred acceptance algorithm to produce a stable matching have desirable properties. The second component incorporates incomplete cardinal information in the school choice problem by considering students with private valuations for schools. Students can have different ordinal rankings of schools while some schools can be more popular than others. In this setting, the research demonstrates that the Boston mechanism does not always result in a higher social welfare than the deferred acceptance algorithm. The project also includes research to uncover the general structure of these mechanisms and to analyze the Bayesian assignment game, another category of school choice problem.