The iterative deferred acceptance mechanism

We introduce a new mechanism for matching students to schools or universities, denoted Iterative Deferred Acceptance Mechanism (IDAM), inspired by procedures currently being used to match millions of students to public universities in Brazil and China. Unlike most options available in the literature, IDAM is not a direct mechanism. Instead of requesting from each student a full preference over all colleges, the student is instead repeatedly asked to choose one college among those which would accept her given the current set of students choosing that college. Although the induced sequential game has no dominant strategy, when students simply choose the most preferred college in each period (denoted the straightforward strategy), the matching that is produced is the Student Optimal Stable Matching. Moreover, under imperfect information, students following the straightforward strategy is an Ordinal Perfect Bayesian Equilibrium. Based on data from 2016, we also provide evidence that, due to shortcomings which are absent in the modified version that we propose, the currently used mechanism in Brazil fails to assist the students with reliable information about the universities that they are able to attend, and are subject to manipulation via cutoffs, a new type of strategic behavior that is introduced by this family of iterative mechanisms and observed in the field.