In recent years, a growing number of students are being assigned to schools through centralized clearinghouses. The success of such clearinghouses crucially relies on the use of a stable matching mechanism [10,12]. The matching market design literature finds that a designer who wishes to implement a stable allocation has limited scope for further design. First, the rural hospital theorem determines that the same positions are filled in all stable allocations [7,9]. Second, the set of stable allocations has the consensus property: all students prefer the outcome of the student-proposing deferred acceptance mechanism (henceforth) to any other stable allocation [4,8]. Third, empirical and theoretical studies suggest that all students, save for a handful, receive the same assignment in all stable allocations [e.g., 1, 2, 5 , 6, 11]. This last finding implies that schools have limited incentive to collect information and to misreport their preferences [3].

Prior to 2014, the admission to Master's and PhD programs in psychology in Israel was a mostly decentralized process. In 2013, in response to concerns about the existing procedure, we proposed to use a mechanism that is both stable and strategy-proof for applicants. The first part of this paper describes how we successfully centralized this market, and the critical role of recent advances in the theory of matching with contracts. In the second part of the paper we show empirically (using clearinghouse data) and theoretically that the regularity in preferences with respect to contractual terms leads to a large core. Our results stand in sharp contrast to findings of previous studies on two-sided matching markets without contracts [2, 10, 11, 13]. During the design of the Israeli Psychology Master's Match (IPMM), we met with the faculty of each of the participating programs and asked about the way they choose between applicants. We discovered that departments' choice functions cannot be summarized by a quota and a rank-ordered list (ROL) for each program. Some departments employ affirmative action through minority quotas. Others aim to equalize the number of advisees each faculty member receives. And finally, some departments are willing to admit a limited number of applicants with different contractual terms (e.g., funding). Since terms can alter preferences between programs, this last feature implies that in order to satisfy the aforementioned desiderata, the applicants' message space must be expressive enough to convey their preferences over program-terms pairs. This market is therefore a special case of the matching-with-contracts model [9].

A mechanism is said to be strategy-proof if no agent has an incentive to misrepresent her true preferences. This property is considered highly desirable for mechanisms that are used in real-life markets. And indeed, many of the great success stories of market design employ strategy-proof mechanisms, such as the second-price sealed-bid auction (Vickrey 1961), or Deferred Acceptance (DA, Gale and Shapley 1962; Dubins and Freedman 1981; Roth 1982). Specifically, in school-choice settings, the appeal of strategy-proof mechanisms is one of the main reasons many school districts choose the applicant-proposing version of DA over pre-existing mechanisms. At the core of the attractiveness of these mechanisms is the assumption that agents report their preferences truthfully in strategy-proof environments.

School choice districts that implement stable matchings face various design issues that impact students' assignments to schools. We study properties of the rank distribution of students with random preferences, when schools use different tiebreaking rules to rank equivalent students. We find that under a multiple tiebreaking rule a vanishing fraction of students match to one of their top choices, in contrast to a single tiebreaking rule under which a constant fraction of students are assigned to one of their top choices. We find that when students can submit only a relatively short preference list, the multiple tiebreaking rule allows a constant fraction of students to match to one of their top choices, with only a "small" fraction of students remaining unmatched.

No abstract available.

The "law of one price" asserts that homogeneous goods must sell for the same price across locations and vendors. While many deviations from this 'law' have been observed in the real world, it remains a useful building block in economic theory, and serves as a benchmark for empirical studies. A crucial underlying assumption used in arguing for the validity of the law is the homogeneity of goods and buyers: buyers do not care which of the goods they buy, or which seller they are buying it from, nor do sellers care about the identity of the buyers. In other words, any two instances of the good are perfect substitutes for the buyers, as are any two buyers from any seller's point of view. This paper makes the formal claim that even in the presence of heterogeneous preferences, an approximate version of the law remains valid, and the approximation improves as the market grows large.