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.

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.

Stability in Matching Markets with Complex Constraints

We develop a model of many-to-one matching markets in which agents with multiunit demand aim to maximize a cardinal linear objective subject to multidimensional knapsack constraints. The choice functions of agents with multiunit demand are therefore not substitutable. As a result, pairwise stable matchings may not exist and even when they do, may be highly inefficient. We provide an algorithm that finds a group-stable matching that approximately satisfies all the multidimensional knapsack constraints. The novel ingredient in our algorithm is a combination of matching with contracts and Scarf’s Lemma. We show that the degree of the constraint violation under our algorithm is proportional to the sparsity of the constraint matrix. The algorithm, therefore, provides practical constraint violation bounds for applications in contexts, such as refugee resettlement, day care allocation, and college admissions with diversity requirements. Simulations using refugee resettlement data show that our approach produces outcomes that are not only more stable, but also more efficient than the outcomes of the Deferred Acceptance algorithm. Moreover, simulations suggest that in practice, constraint violations under our algorithm would be even smaller than the theoretical bounds. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Deferred Acceptance with Compensation Chains

In a foundational paper, Gale and Shapley (1962) introduced the deferred acceptance algorithm that achieves a stable outcome in a two-sided matching market by letting one side of the market make proposals to the other side. What happens when both sides of the market can propose? In “Deferred Acceptance with Compensation Chains,” Dworczak answers this question by constructing an equitable version of the Gale–Shapley algorithm in which the sequence of proposers can be arbitrary. The main result of the paper shows that the extended algorithm, equipped with so-called compensation chains, is not only guaranteed to converge in polynomial time to a stable outcome, but—in contrast to the original Gale–Shapley algorithm—achieves all stable matchings (as the sequence of proposers vary). The proof of convergence uses a novel potential function. The algorithm may find applications in settings where both stability and fairness are desirable features of the matching process.

Heterogeneous Beliefs and School Choice Mechanisms

This paper studies how welfare outcomes in centralized school choice depend on the assignment mechanism when participants are not fully informed. Using a survey of school choice participants in a strategic setting, we show that beliefs about admissions chances differ from rational expectations values and predict choice behavior. To quantify the welfare costs of belief errors, we estimate a model of school choice that incorporates subjective beliefs. We evaluate the equilibrium effects of switching to a strategy-proof deferred acceptance algorithm, and of improving households’ belief accuracy. We find that a switch to truthful reporting in the DA mechanism offers welfare improvements over the baseline given the belief errors we observe in the data, but that an analyst who assumed families had accurate beliefs would have reached the opposite conclusion. (JEL D83, H75, I21, I28)