Quantile Stable Mechanisms

We introduce a new class of matching mechanisms—quantile stable mechanisms—that generate stable matchings that can be seen as a compromise between sides of a two-sided market. We show that responsiveness is a sufficient condition for the existence of such mechanisms and that all such mechanisms are distinct. We also analyze the manipulability of these mechanisms by market participants.

Stability and Median Rationalizability for Aggregate Matchings

We develop the theory of stability for aggregate matchings used in empirical studies and establish fundamental properties of stable matchings including the result that the set of stable matchings is a non-empty, complete, and distributive lattice. Aggregate matchings are relevant as matching data in revealed preference theory. We present a result on rationalizing a matching data as the median stable matching.

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.

Pairwise Stable Matching in Large Economies

We formulate a stability notion for two‐sided pairwise matching problems with individually insignificant agents in distributional form. Matchings are formulated as joint distributions over the characteristics of the populations to be matched. Spaces of characteristics can be high‐dimensional and need not be compact. Stable matchings exist with and without transfers, and stable matchings correspond precisely to limits of stable matchings for finite‐agent models. We can embed existing continuum matching models and stability notions with transferable utility as special cases of our model and stability notion. In contrast to finite‐agent matching models, stable matchings exist under a general class of externalities.