Static versus dynamic deferred acceptance in school choice: Theory and experiment

Abstract

In the context of school choice, we experimentally study how behavior and outcomes are affected when, instead of submitting rankings in the student proposing or receiving deferred acceptance (DA) mechanism, participants make decisions dynamically, going through the steps of the underlying algorithms. Our main results show that, contrary to theory, (a) in the dynamic student proposing DA mechanism, participants propose to schools respecting the order of their true preferences slightly more often than in its static version while, (b) in the dynamic student receiving DA mechanism, participants react to proposals by always respecting the order and not accepting schools in the tail of their true preferences more often than in the corresponding static version. As a consequence, for most problems we test, no significant differences exist between the two versions of the student proposing DA mechanisms in what stability and average payoffs are concerned, but the dynamic version of the student receiving DA mechanism delivers a clear improvement over its static counterpart in both dimensions. In fact, in the aggregate, the dynamic school proposing DA mechanism is the best performing mechanism.

Experiments on centralized school choice and college admissions: a survey

“…Eight students competed for seats at eight colleges with one seat each. In contrast to Klijn et al (2019), they find that under iterative DA stable allocations are reached significantly more often than under static DA. The difference is driven by a significantly higher proportion of subjects behaving truthfully in the iterative mechanism.…”

“…The results of both Bó and Hakimov (2020a) and Klijn et al (2019) indicate a failure of the theoretical prediction of more truthful behavior under static mechanisms. 21 Bó and Hakimov (2020a) investigate different possible explanations for the observed difference between static and dynamic DA and conclude that the advantage of dynamic DA is the feedback it provides after every step (rejection from the previously applied university) and the possibility to re-strategize given this feedback.…”

“…The first two studies reported on in this subsection by Klijn et al (2019) and Bó and Hakimov (2020a) consider the iterative DA mechanism. Instead of submitting rank-order lists before the algorithms starts as in static DA, under iterative DA the proposing side makes one proposal at a time.…”

“…Following the literature, we use the terms "iterative" and "dynamic" interchangeably to refer to this modification of DA. Klijn et al (2019) compare the student-and school-proposing DA to their iterative counterparts. 20 The experiment implements a one-sided matching setup where the schools were played by the computer and always behaved truthfully (either by proposing in the order of priorities or by choosing among proposals according to their priorities).…”

“…In a closely related paper by Bó and Hakimov (2020a), the authors also compare static and iterative versions of student-proposing DA. Unlike Klijn et al (2019), they implemented incomplete information about the priorities, i.e., participants only knew their grades for each university, but not the grades of other students. They knew, however, the distribution of the grades.…”