Communication Requirements and Informative Signaling in Matching Markets

Abstract

We study how much communication is needed to find a stable matching in a two-sided matching market with private preferences. Segal (2007) and Gonczarowski et al.~(2015) showed that in the worst case, any protocol that computes a stable matching requires the communication cost per agent to scale linearly in the total number of agents. In real-world markets with many agents, this communication requirement is implausibly high. This casts doubts on whether stable matching can arise in large markets. We study markets with realistic structure on the preferences and information of agents, and show that in "typical" markets, a stable matching can be found with much less communication effort. In our model, the preferences of workers are unrestricted, and the preferences of firms follow an additively separable latent utility model. Our efficient communication protocol modifies workers-proposing DA, by having firms signal workers they especially like, while also broadcasting qualification requirements to discourage other workers who have no realistic chances from applying. In the special case of tiered random markets, the protocol can be modified to run in two-rounds and involve only private messages. Our protocols have good incentive properties and give insights on how to mediate large matching markets to reduce congestion.