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Stable matching as transport (2402.13378v2)

Published 20 Feb 2024 in econ.TH and cs.GT

Abstract: This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter reflects society's preferences for inequality. This link offers insights into structural properties of matchings and trade-offs between objectives; showing how stability can lead to welfare inequalities, even among similar agents. Our model captures supply-demand imbalances in contexts like spatial markets, school choice, and ride-sharing. We also show that large markets with idiosyncratic preferences can be well approximated by aligned preferences, expanding the applicability of our results.

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  1. Uniqueness of stable matchings without large indifference sets
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