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18-05-2021 | Original Paper | Issue 4/2021

Social Choice and Welfare 4/2021

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

Journal:
Social Choice and Welfare > Issue 4/2021
Authors:
Flip Klijn, Markus Walzl, Christopher Kah
Important notes
The first draft of this paper was written while F. Klijn was LFUI guest professor at Innsbruck University. He gratefully acknowledges the hospitality of Innsbruck University and support from AGAUR-Generalitat de Catalunya (2017-SGR-1359), Ministerio de Ciencia, Innovación y Universidades (ECO2017-88130-P), and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563 and CEX2019-000915-S). C. Kah and M. Walzl thank the Austrian Science Foundation (FWF) for support through project P-28632-G27 and SFB63. We thank two reviewers, Péter Biró, Lars Ehlers, Pau Milán, Anne van den Nouweland, and seminar and workshop participants at Université de Lausanne, the Dutch Social Choice Colloquium (Maastricht, 2019), 24th Coalition Theory Network Workshop (Aix-en-Provence), and Conference on Economic Design 2019 (Budapest) for useful comments and suggestions. We are particularly grateful to the reviewer who suggested an alternative global distance, as discussed in Sect. 5

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Abstract

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.

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