Here's an interesting new paper on couples in matching markets. When couples are present, the set of stable matchings may be empty, but a "small" perturbation of the problem that increases the capacities of some employers and decreases the capacity of others, restores the existence of stable matchings. (I haven't yet fully absorbed this, e.g. its impact on overall employment...)
Near Feasible Stable Matchings with Complementarities
Near Feasible Stable Matchings with Complementarities
Thanh Nguyen and Rakesh Vohra
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