We report on the centralization of a two-sided matching-with-contracts market, in which pre-existing choice functions violate the substitutes condition. The ability to accommodate these choice functions was critical for the success of our design. The new mechanism is stable and strategy-proof for applicants. It is well accepted by both sides of the market. Our study provides a strong empirical validation for the practical relevance of recent theoretical advances on matching without substitutes.

Honesty is the best policy in the face of a strategy-proof mechanism--irrespective of others' behavior, the best course of action is to report one's preferences truthfully. We review evidence from different markets in different countries and find that a substantial percentage of participants do not report their true preferences to the strategy-proof Deferred Acceptance mechanism. Two recurring correlates of preference misrepresentation are lower cognitive ability and the expectation of stronger competition. We evaluate possible explanations, which we hope will inform practicing market designers.

We study college admissions markets where students can attend the same college under different financial terms. The deferred acceptance algorithm identifies a stable allocation where funding is allocated based on merit and the set of meritbased stable allocations is small. When students are heterogeneous in the way they trade off program characteristics and contractual terms, the set of stable allocations is large and different stable allocations differ in the number of assigned students. In Hungary, where such heterogeneity is present, a non-merit-based stable allocation would increase the number of assigned applicants by 1.9% relative to any merit-based stable allocation.