This paper characterizes the top trading cycles mechanism for the school choice problem. Schools may have multiple available seats to be assigned to students. For each school a strict priority ordering of students is determined by the school district. Each student has strict preference over the...

The Boston mechanism is among the most popular school choice procedures in use. Yet, the mechanism has been criticized for its poor incentive and welfare performances, which led the Boston Public Schools to recently replace it with Gale and Shapley's deferred acceptance algorithm (henceforth,...

The Boston mechanism is among the most popular school choice procedures in use. Yet, the mechanism has been criticized for its poor incentive and welfare performances, which led the Boston Public Schools to recently replace it with Gale and Shapley's deferred acceptance algorithm (henceforth,...

We consider a priority based allocation problem with general weak priorities. We focus on two strategy-proof mechanisms: the deferred acceptance (DA) mechanism and the top trading cycles (TTC) mechanism. We give two conditions on weak priority structures whereby each of the DA mechanism and TTC...

We revisit the school choice problem with consent proposed by Kesten (2010), which seeks to improve the efficiency of the student-optimal deferred acceptance algorithm (DA) by obtaining students' consent to give up their priorities. We observe that for students to consent, we should use their...

For school choice (priority-based allocation) problems, when the priority structure is acyclic, the associated student-proposing deferred acceptance algorithm is Pareto efficient and group strategy-proof (Ergin, 2002). We reveal a hidden iterative removal structure behind such deferred...

We revisit the school choice problem with affirmative action policies, or more generally, the controlled school choice problem proposed by Abdulkadiroglu and Sönmez (2003), and furtherly developed by Kojima (2012). The latter investigates the welfare effects of affirmative action policies and...

The prevalent affirmative action policy in school choice limits the number of admitted majority students to give minority students higher chances to attend their desired schools. There have been numerous efforts to reconcile affirmative action policies with celebrated matching mechanisms such as...

A set of indivisible objects is allocated among agents with strict preferences. Each object has a weak priority ranking of the agents. A collection of priority rankings, a priority structure, is solvable if there is a strategy-proof mechanism that is constrained efficient, i.e. that always...

We generalize the school choice problem by defining a notion of allowable priority violations. In this setting, a weak axiom of stability (partial stability) allows only certain priority violations. We introduce a class of algorithms called the Student Exchange under Partial Fairness (SEPF)....