Continuity of stable marriage correspondences

Will Sandholtz and Andrew Tai

Papers from arXiv.org

Abstract: We study a continuum version of the stable marriage problem, in which each agent has a variable mass to be paired to the opposite side. An agent's mass is interpretable as the divisible time of a single atomistic agent, or as a mass of infinitesimal agents of a particular type. Our object of interest is the mapping between the vector of masses to the set of stable matches. As in the canonical stable marriage model, the set of stable matches can be multi-valued, so this mapping is a correspondence. This correspondence is continuous if and only if the stable match is unique, implying that small changes in the masses may cause discontinuous jumps in the set of stable matches.

Date: 2026-10
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