Almost mutually best in matching markets: rank gaps and size of the core

Authors: Flip Klijn, Markus Walzl and Christopher Kah

Social Choice and Welfare, Vol. 57, 797–816 , May, 2021

This paper studies the one-to-one two-sided marriage model (Gale and Shapley 1962). If agents’ preferences exhibit mutually best (i.e., each agent is most preferred by her/his most preferred matching partner), there is a unique stable matching without rank gaps (i.e., in each matched pair the agents assign one another the same rank). We study in how far this result is robust for matching markets that are “close” to mutually best. Without a restriction on preference profiles, we find that natural “distances” to mutually best neither bound the size of the core nor the rank gaps at stable matchings. However, for matching markets that satisfy horizontal heterogeneity, “local” distances to mutually best provide bounds for the size of the core and the rank gaps at stable matchings.

This paper originally appeared as Barcelona School of Economics Working Paper 1115