Matching through institutions

We model a matching market with institutions -inspired by the assignment of social housing in Paris- as a three-sided market. Institutions own objects and have agents attached to them. Agents have preferences over objects. Objects have priorities over institutions. We show that fair assignments satisfying distributional constraints may fail to exist, and propose a sufficient condition -the over-demand condition- under which we prove existence. Existence derives from the construction of a new algorithm, the Nested Deferred Acceptance (NDA) algorithm, which combines a one-to-one matching between agents and objects and a one-to-many matching between objects and institutions. If interrupters are eliminated from the preference list, as in Kesten (2010), the NDA algorithm produces an assignment which is fair, Pareto optimal among fair assignments and strategy-proof for agents.

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