Almost Mutually Best in Matching Markets: Rank-Fairness and Size of the Core

Abstract

This paper studies the one-to-one two-sided marriage model (Gale and Shapley, 1962). If agents' preferences exhibit mutually best, there is a unique stable matching that is trivially rank-fair (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-unfairness of 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- unfairness of stable matchings.