Efficient Matchmaking in Assignment Games with Application to Online Platforms

Abstract

An assignment game is a model of two-sided markets with transfer payments, and can be used to study the matching between heterogeneous customers and service providers with endogenous determination of prices. We study how a market intermediary can best facilitate matches in an assignment game so as to achieve a good outcome while minimizing the number of bits of information agents need to communicate. Here, "good outcomes" are formalized as ε-stable, which means that no pair of agents can deviate and both benefit by more than ε. We show that an ε-stable outcome can be found using only O(log n) bits of communication per agent whenever the horizontal component of one side's preferences is predictable or dense. ("Dense" means that those agents have high preferences for many potential partners.) But matchmaking requires Ω(sqrt{n}) bits per agent when the horizontal preferences of both sides are unpredictable and sparse, meaning that both sides have high preferences only for a vanishing proportion of the market. We propose near optimal sequential protocols for both dense and sparse preferences, as well as a near-optimal simultaneous protocol for thick markets with dense preferences on both sides. The protocols yield prescriptive insights for online platforms in the home services industry.

Keywords: market design, online platforms, two-sided matching, communication complexity

JEL Classification: D47, D83, C78