Umut Mert Dur

A Characterization of the Top Trading Cycles Mechanism for the School Choice Problem

Abstract 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 schools. We first define weaker forms of fairness, consistency and resource monotonicity. We show that the top trading cycles mechanism is the unique Pareto efficient and strategy-proof mechanism that satisfies the weaker forms of fairness, consistency and resource monotonicity. To our knowledge this is the first axiomatic approach to the top trading cycles mechanism in the school choice problem where schools have a capacity greater than one.

Reserve Design: Unintended Consequences and the Demise of Boston's Walk Zones

We show that in the presence of admissions reserves, the effect of the precedence order (i.e., the order in which different types of seats are filled) is comparable to the effect of adjusting reserve sizes. Either lowering the precedence of reserve seats at a school or increasing the school’s reserve size weakly increases reserve-group assignment at that school. Using data from Boston Public Schools, we show that reserve and precedence adjustments have similar quantitative effects. Transparency about these issues—in particular, how precedence unintentionally undermined intended policy—led to the elimination of walk zone reserves in Boston’s public school match.

Two-Sided Matching via Balanced Exchange: Tuition and Worker Exchanges

We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchange, in which each firm has to avoid being a net-exporter of workers. These exchanges use decentralized markets, making it difficult to achieve a balance between exports and imports. We show that stable equilibria discourage net-exporting firms from exchange. We introduce the two-sided top-trading-cycles mechanism that is balanced-efficient, worker-strategy-proof, acceptable, and individually rational, and respects priority bylaws regarding worker eligibility. We prove that it is the unique mechanism fulfilling these objectives. Moreover, it encourages exchange, since full participation is the dominant strategy for firms.When an institution participates in the Tuition Exchange Scholarship program, it will offer a tuition waiver for up to four years (eight semesters) of full-time baccalaureate degree study, provided the student maintains continuing eligibility. If tuition at the awarding college or university is less than

Competitive equilibria in school assignment

37,000, the scholarship will cover the full amount of tuition. If the tuition at the institution exceeds

Two-Sided Matching via Balanced Exchange

37,000, the minimum Tuition Exchange scholarship will be

First-Choice Maximal and First-Choice Stable School Choice Mechanisms

37,000, although many colleges will cover the full tuition amount. Room, board and fees are not usually included in the scholarship offered by host institutions; however, there are exceptions. Institutions with high tuition may award less than full tuition (but not less than

College Admissions with Complementarities

37,000 for the 2019-2020 academic year).

When Manipulations Are Harm[less]ful?

Top Trading Cycles was originally developed as an elegant method for finding a competitive equilibrium of Shapley and Scarfs housing market. We extend the definition of a competitive equilibrium to the school assignment problem and show that there remains a profound relationship between Top Trading Cycles and a competitive equilibrium. Specifically, in every competitive equilibrium with weakly decreasing prices, the equilibrium assignment is unique and exactly corresponds to the Top Trading Cycles assignment. This provides a new way of interpreting the worth of a students priority at a given school. It also provides a new way of explaining Top Trading Cycles to students and a school board.

A 1.5-Sided Matching Problem: The Cost-Efficient House Allocation Problem with Existing Tenants

We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchanges, in which export-import balances are required for longevity of programs. These exchanges use decentralized markets, making it difficult to achieve this goal. We introduce the two-sided top trading cycles, the unique mechanism that is balanced-efficient, worker-strategy-proof, acceptable, individually rational, and respecting priority bylaws regarding worker eligibility. Moreover, it encourages exchange, because full participation induces a dominant-strategy equilibrium for firms. We extend it to dynamic settings permitting tolerable yearly imbalances and demonstrate that its regular and tolerable versions perform considerably better than models of current practice.

The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice

We investigate the class of school choice mechanisms that are first-choice maximal (FCM) (i.e., they match a maximal number of students to their reported first choices) and first-choice stable (FCS) (i.e., no students form blocking pairs with their reported first choices). FCM is a ubiquitous desideratum in school choice, and we show that FCS is the only rank-based relaxation of stability that is compatible with FCM. The class of FCM and FCS mechanisms includes variants of the well-known Boston mechanism as well as certain Asymmetric Chinese Parallel mechanisms. Regarding incentives, we show that while no mechanism in this class is strategyproof, the Pareto efficient ones are least susceptible to manipulation. Regarding student welfare, we show that the Nash equilibrium outcomes of these mechanisms correspond precisely to the set of stable matchings. By contrast, when some students are sincere, we show that more students may be matched to their true first choices in equilibrium than under any stable matching. Finally, we show how our results can be used to obtain a new characterization of the Boston mechanism (i.e., the most widely used FCM and FCS mechanism). On a technical level, this paper provides new insights about an influential class of school choice mechanisms. For practical market design, our results yield a potential rationale for the popularity of FCM and FCS mechanisms in practice.