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.
