This article analyzes the provision of matching services in a model of two-sided search. Agents belong to two heterogeneous populations and are distributed on [0, 1]. Their utility is equal to the index of their mate. In a search equilibrium agents form subintervals and are only matched to agents inside their class. Marriage brokers match agents according to a centralized procedure. If the matchmaker charges a uniform participation fee, only agents of higher quality participate in the centralized procedure. If the matchmaker charges a commission on the matching surplus, only agents of lower quality go to the intermediary.
Bloch, F., & Ryder, H. (2000). Two-sided search, marriages, and matchmakers. International Economic Review, 41(1), 93-115. https://doi.org/10.1111/1468-2354.00056 (Original work published 2000)