Two-Sided Random Matching Markets: Ex-Ante Equivalence of the Deferred Acceptance Procedures

Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal work by Gale and Shapley. When the input preference profile is generated from a distribution, we study the output distribution of two stable matching procedures: women-proposing-deferred-acceptance and men-proposing-deferred-acceptance. We show that the two procedures are ex-ante equivalent—that is, under certain conditions on the input distribution, their output distributions are identical. In terms of technical contributions, we generalize (to the non-uniform case) an integral formula, due to Knuth and Pittel, which gives the probability that a fixed matching is stable. Using an inclusion-exclusion principle on the set of rotations, we give a new formula that gives the probability that a fixed matching is the women/men-optimal stable matching.

A deferred acceptance mechanism for decentralized, fast, and fair childcare assignment

We design and implement a program-proposing deferred acceptance mechanism with ties (DAT) and apply it to childcare assignment in two German cities. The mechanism can accommodate complementarities in providers' preferences, is fast to terminate even in larger cities, is difficult to manipulate in practice, and produces stable allocations. It can be further sped up by introducing two new features. First, allowing for an arbitrary share of facilities who participate in a centralized manner by submitting a rank-order-list over applicants. Second, by breaking ties in applicants' rank-order-lists on a first-come-first-serve basis, which sets incentives for programs to propose faster. We provide and evaluate simulation results.

A Feasible Solution for Rebalancing Large-Scale Bike Sharing Systems

City bikes and bike-sharing systems (BSSs) are one solution to the last mile problem. BSSs guarantee equity by presenting affordable alternative transportation means for low-income households. These systems feature a multitude of bike stations scattered around a city. Numerous stations mean users can borrow a bike from one location and return it there or to a different location. However, this may create an unbalanced system, where some stations have excess bikes and others have limited bikes. In this paper, we propose a solution to balance BSS stations to satisfy the expected demand. Moreover, this paper represents a direct extension of the deferred acceptance algorithm-based heuristic previously proposed by the authors. We develop an algorithm that provides a delivery truck with a near-optimal route (i.e., finding the shortest Hamiltonian cycle) as an NP-hard problem. Results provide good solution quality and computational time performance, making the algorithm a viable candidate for real-time use by BSS operators. Our suggested approach is best suited for low-Q problems. Moreover, the mean running times for the largest instance are 143.6, 130.32, and 51.85 s for Q = 30, 20, and 10, respectively, which makes the proposed algorithm a real-time rebalancing algorithm.

The Effect of Attending a Charter School in Newark, New Jersey, on Student Test Scores

We exploit information about parental preference and a randomized component in the assignment of students to schools within a deferred acceptance (DA) mechanism to estimate the causal effect of enrolling in a charter school in Newark, New Jersey, on student test scores. The estimates incorporate variation from students attending about 70% of the city’s charter schools, accounting for about 85% of charter school enrollment. Enrolling in a Newark charter school that participated in the DA assignment process leads to a large and statistically significant increase in math and English Language Arts (ELA) scores. Enrolling in a charter school that is operated by either the Knowledge Is Power Program (KIPP) or Uncommon charter school networks has an especially large effect.

Accomplice Manipulation of the Deferred Acceptance Algorithm

The deferred acceptance algorithm is an elegant solution to the stable matching problem that guarantees optimality and truthfulness for one side of the market. Despite these desirable guarantees, it is susceptible to strategic misreporting of preferences by the agents on the other side. We study a novel model of strategic behavior under the deferred acceptance algorithm: manipulation through an accomplice. Here, an agent on the proposed-to side (say, a woman) partners with an agent on the proposing side---an accomplice---to manipulate on her behalf (possibly at the expense of worsening his match). We show that the optimal manipulation strategy for an accomplice comprises of promoting exactly one woman in his true list (i.e., an inconspicuous manipulation). This structural result immediately gives a polynomial-time algorithm for computing an optimal accomplice manipulation. We also study the conditions under which the manipulated matching is stable with respect to the true preferences. Our experimental results show that accomplice manipulation outperforms self manipulation both in terms of the frequency of occurrence as well as the quality of matched partners.

Information acquisition and provision in school choice: a theoretical investigation

When participating in school choice, students may incur information acquisition costs to learn about school quality. This paper investigates how two popular school choice mechanisms, the (Boston) Immediate Acceptance and the Deferred Acceptance, incentivize students’ information acquisition. Specifically, we show that only the Immediate Acceptance mechanism incentivizes students to learn their own cardinal and others’ preferences. We demonstrate that information acquisition costs affect the efficiency of each mechanism and the welfare ranking between the two. In the case where everyone has the same ordinal preferences, we evaluate the welfare effects of various information provision policies by education authorities.