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Fragile Stable Matchings

Published 18 Mar 2024 in econ.TH and cs.GT | (2403.12183v1)

Abstract: We show how fragile stable matchings are in a decentralized one-to-one matching setting. The classical work of Roth and Vande Vate (1990) suggests simple decentralized dynamics in which randomly-chosen blocking pairs match successively. Such decentralized interactions guarantee convergence to a stable matching. Our first theorem shows that, under mild conditions, any unstable matching -- including a small perturbation of a stable matching -- can culminate in any stable matching through these dynamics. Our second theorem highlights another aspect of fragility: stabilization may take a long time. Even in markets with a unique stable matching, where the dynamics always converge to the same matching, decentralized interactions can require an exponentially long duration to converge. A small perturbation of a stable matching may lead the market away from stability and involve a sizable proportion of mismatched participants for extended periods. Our results hold for a broad class of dynamics.

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  1. Kirill Rudov 

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