Multiperiod Matching

Abstract

We examine a dynamic, two‐sided, one‐to‐one matching market where agents on both sides interact over a period of time. We define and identify sufficient conditions for the existence of a dynamically stable matching, which may require revisions to initial assignments. A generalization of the deferred acceptance algorithm can identify dynamically stable outcomes in a large class of economies, including cases with intertemporal preference complementarities. We relate our analysis to market unraveling and to common market design applications, including the medical residency match.

Dynamic Many-to-One Matching

“…Therefore, we provide an alternative explanation of why the US college system has used some form of early admissions for a century. 10 Thus, we conclude that the choice of a stable matching algorithm might affect the "level" of unraveling.…”

“…She identifies the trade-off between matching today and waiting for a better option in an environment where matchings cannot be revised. In other studies, matching opportunities are fixed, whereas pairings can be revised over time: Damiano and Lam (2005), Kurino (2009), Kadam & Kotowski (2018), Kotowski (2019), Liu (2018), and Pereyra (2013). Our contribution to this literature is to introduce a suitable group stability notion for many-toone matching markets where matchings form over time and are irreversible.…”

“…The prominent examples are college admissions, school choice, and entry-level professional labor markets such as medical residency matching. 3 Researchers have studied dynamic one-to-one matching environments: Doval (2019), Kadam & Kotowski (2018), Kurino (2009), Baccara et al (2016), and so on. This paper is the first to analyze dynamic many-to-one matching markets with irreversible matches.…”

Stability against robust deviations in the roommate problem

“…While we investigate a static model with dynamic arguments as a possible interpretation and motivation, Kadam and Kotowski (2018) and Kotowski (2015) explicitly study a dynamic marriage market, where agents have their preferences over the histories (i.e., sequences) of matched partners. They also define stability concepts for their dynamic setting, but it should be noted that their concepts reduce to the standard stability in the static setting.…”

A Compact, Logical Approach to Large-Market Analysis

“…5 In each setting we consider, we give what can be thought of as minimal working examples; it seems likely that Compactness can be used to further generalize results in these and other settings, as well (even before translating into topological statements as discussed above). For example, we suspect that the approach we use in Section 4 should translate directly to other dynamic matching models (e.g., Doval, 2017;Kadam and Kotowski, 2018), including those with infinitely many periods. It seems logical that the results we present represent just the tip of the iceberg in terms of what the techniques we introduce-and future refinements thereof-should eventually be able to accomplish.…”