Competition and Search Frictions in (Random) Matching Markets

Understanding market equilibria (e.g., stable matchings) enables us to design better markets. Random matching market models have been a popular tool to capture heterogeneous preference rankings in two-sided matching markets. Random markets with an equal number of "men" and "women" exhibit a wide range of stable outcomes, in contrast to the nearly unique outcome seen in real datasets. With Ashlagi and Leshno (2017), we allow an unequal number of agents on the two sides ("imbalance") and find that under the smallest imbalance there is indeed a nearly unique stable outcome, in which the short side essentially chooses. This produces a new mystery: many real datasets do not exhibit a significant short-side advantage. With Min and Qian (2020), we study "partially connected" random markets in which agents consider a limited set of potential partners, and discover a new type of smoking gun evidence of whether a matching market exhibits a short side advantage.

With Immorlica and Lu (2020) we model costly inspections for compatibility prior to matching, towards understanding market "congestion" (inefficiency in partner search). We identify a large class of markets which suffer from "information deadlock" where a significant fraction of agents get stuck waiting for each other to make up their minds prior to inspecting.