Complementarities in childcare allocation under priorities

Abstract: We investigate the allocation of children to childcare facilities and propose solutions to overcome limitations in the current allocation mechanism. We introduce a natural preference domain and a priority structure that address these setbacks, aiming to enhance the allocation process. To achieve this, we present an adaptation of the Deferred Acceptance mechanism to our problem, which ensures strategy-proofness within our preference domain and yields the student-optimal stable matching. Finally, we provide a maximal domain for the existence of stable matchings using the properties that define our natural preference domain. Our results have practical implications for allocating indivisible bundles with complementarities.